Is it possible to find $n^th$ derivative of $frac1e^ax+b$?$n^th$ derivative of $cot x$What is the proof of integral theorem i.e area under curve is given by anti derivative?Struggling to find the second derivative of this function's first derivativelargest interval over which the general solution is definedA fence of $y$ ft is $x$ ft from a wall, find shortest ladder using trigonometryDouble derivative w.r.t x and y neededQuick question regarding $int fraccos x + sin xsin 2x,dx$Find the derivative of: $(f^-1)'(0)$ with $f(x)=int_1^xcos(cos(t))dt$derivative of integralFind the $lim_n to 0 (cos(x)+tan^2(x))^csc(x)$Differentiating $x = sec^23y$ for $d^2y/dx^2$

How to change two letters closest to a string and one letter immediately after a string using notepad++

Why doesn't the EU now just force the UK to choose between referendum and no-deal?

Unexpected result from ArcLength

Does Mathematica reuse previous computations?

Have researchers managed to "reverse time"? If so, what does that mean for physics?

Why is the President allowed to veto a cancellation of emergency powers?

Who is flying the vertibirds?

Time travel from stationary position?

How do I hide Chekhov's Gun?

Professor being mistaken for a grad student

Are there verbs that are neither telic, or atelic?

How can you use ICE tables to solve multiple coupled equilibria?

Is it true that good novels will automatically sell themselves on Amazon (and so on) and there is no need for one to waste time promoting?

Do I need to be arrogant to get ahead?

Why one should not leave fingerprints on bulbs and plugs?

How could a scammer know the apps on my phone / iTunes account?

Gantt Chart like rectangles with log scale

What exactly is this small puffer fish doing and how did it manage to accomplish such a feat?

How to explain that I do not want to visit a country due to personal safety concern?

Is a party consisting of only a bard, a cleric, and a warlock functional long-term?

It's a yearly task, alright

Life insurance that covers only simultaneous/dual deaths

(Calculus) Derivative Thinking Question

A sequence that has integer values for prime indexes only:



Is it possible to find $n^th$ derivative of $frac1e^ax+b$?


$n^th$ derivative of $cot x$What is the proof of integral theorem i.e area under curve is given by anti derivative?Struggling to find the second derivative of this function's first derivativelargest interval over which the general solution is definedA fence of $y$ ft is $x$ ft from a wall, find shortest ladder using trigonometryDouble derivative w.r.t x and y neededQuick question regarding $int fraccos x + sin xsin 2x,dx$Find the derivative of: $(f^-1)'(0)$ with $f(x)=int_1^xcos(cos(t))dt$derivative of integralFind the $lim_n to 0 (cos(x)+tan^2(x))^csc(x)$Differentiating $x = sec^23y$ for $d^2y/dx^2$













2












$begingroup$



Is it possible to find $n^th$ derivative of $frac1e^ax+b$ ?




I am introduced to $n^th$ differentiation and leibniz theorem as a first year undergraduate.
But what i observe is there are some explicit formula for the $n^th$ derivative of $sin x$,$cos x$,$log(ax+b)$,$frac1ax+b$, etc but why there isn't any method given for $sec x$, $csc x$ etc.



If the highlighted question can be answered then it is possible to find the $n^th$ derivative of secx.
How ?
$$y=sec x=frac1cos x=frac2 e^ixe^2ix+1$$
Now one can use lebniz theorem of $n^th$ differentiation to find the n derivative of product of two functions whose general derivative is known. Now here $e^ix$ whose derivative can be found easily. The latter part $frac1e^2ix+1$ is not known.






calculus algebra-precalculus derivatives







share|cite|improve this question











$endgroup$











  • $begingroup$
    If $y=frac1e^ax+b$, then $y'= a b y^2 - a y$. Perhaps this helps.
    $endgroup$
    – lhf
    Mar 12 at 0:16










  • $begingroup$
    How good is that , differentiation of $n$ times of this will yield its n-th derivative in terms of n-1th or less.
    $endgroup$
    – M Desmond
    Mar 12 at 15:20











  • $begingroup$
    For $cot x$, see math.stackexchange.com/questions/1701540/…
    $endgroup$
    – lhf
    2 days ago
















2












$begingroup$



Is it possible to find $n^th$ derivative of $frac1e^ax+b$ ?




I am introduced to $n^th$ differentiation and leibniz theorem as a first year undergraduate.
But what i observe is there are some explicit formula for the $n^th$ derivative of $sin x$,$cos x$,$log(ax+b)$,$frac1ax+b$, etc but why there isn't any method given for $sec x$, $csc x$ etc.



If the highlighted question can be answered then it is possible to find the $n^th$ derivative of secx.
How ?
$$y=sec x=frac1cos x=frac2 e^ixe^2ix+1$$
Now one can use lebniz theorem of $n^th$ differentiation to find the n derivative of product of two functions whose general derivative is known. Now here $e^ix$ whose derivative can be found easily. The latter part $frac1e^2ix+1$ is not known.






calculus algebra-precalculus derivatives







share|cite|improve this question











$endgroup$











  • $begingroup$
    If $y=frac1e^ax+b$, then $y'= a b y^2 - a y$. Perhaps this helps.
    $endgroup$
    – lhf
    Mar 12 at 0:16










  • $begingroup$
    How good is that , differentiation of $n$ times of this will yield its n-th derivative in terms of n-1th or less.
    $endgroup$
    – M Desmond
    Mar 12 at 15:20











  • $begingroup$
    For $cot x$, see math.stackexchange.com/questions/1701540/…
    $endgroup$
    – lhf
    2 days ago














2












2








2


0



$begingroup$



Is it possible to find $n^th$ derivative of $frac1e^ax+b$ ?




I am introduced to $n^th$ differentiation and leibniz theorem as a first year undergraduate.
But what i observe is there are some explicit formula for the $n^th$ derivative of $sin x$,$cos x$,$log(ax+b)$,$frac1ax+b$, etc but why there isn't any method given for $sec x$, $csc x$ etc.



If the highlighted question can be answered then it is possible to find the $n^th$ derivative of secx.
How ?
$$y=sec x=frac1cos x=frac2 e^ixe^2ix+1$$
Now one can use lebniz theorem of $n^th$ differentiation to find the n derivative of product of two functions whose general derivative is known. Now here $e^ix$ whose derivative can be found easily. The latter part $frac1e^2ix+1$ is not known.






calculus algebra-precalculus derivatives







share|cite|improve this question











$endgroup$





Is it possible to find $n^th$ derivative of $frac1e^ax+b$ ?




I am introduced to $n^th$ differentiation and leibniz theorem as a first year undergraduate.
But what i observe is there are some explicit formula for the $n^th$ derivative of $sin x$,$cos x$,$log(ax+b)$,$frac1ax+b$, etc but why there isn't any method given for $sec x$, $csc x$ etc.



If the highlighted question can be answered then it is possible to find the $n^th$ derivative of secx.
How ?
$$y=sec x=frac1cos x=frac2 e^ixe^2ix+1$$
Now one can use lebniz theorem of $n^th$ differentiation to find the n derivative of product of two functions whose general derivative is known. Now here $e^ix$ whose derivative can be found easily. The latter part $frac1e^2ix+1$ is not known.






calculus algebra-precalculus derivatives




calculus algebra-precalculus derivatives






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Mar 11 at 19:26







M Desmond

















asked Mar 11 at 19:17









M DesmondM Desmond

1587




1587











  • $begingroup$
    If $y=frac1e^ax+b$, then $y'= a b y^2 - a y$. Perhaps this helps.
    $endgroup$
    – lhf
    Mar 12 at 0:16










  • $begingroup$
    How good is that , differentiation of $n$ times of this will yield its n-th derivative in terms of n-1th or less.
    $endgroup$
    – M Desmond
    Mar 12 at 15:20











  • $begingroup$
    For $cot x$, see math.stackexchange.com/questions/1701540/…
    $endgroup$
    – lhf
    2 days ago

















  • $begingroup$
    If $y=frac1e^ax+b$, then $y'= a b y^2 - a y$. Perhaps this helps.
    $endgroup$
    – lhf
    Mar 12 at 0:16










  • $begingroup$
    How good is that , differentiation of $n$ times of this will yield its n-th derivative in terms of n-1th or less.
    $endgroup$
    – M Desmond
    Mar 12 at 15:20











  • $begingroup$
    For $cot x$, see math.stackexchange.com/questions/1701540/…
    $endgroup$
    – lhf
    2 days ago
















$begingroup$
If $y=frac1e^ax+b$, then $y'= a b y^2 - a y$. Perhaps this helps.
$endgroup$
– lhf
Mar 12 at 0:16




$begingroup$
If $y=frac1e^ax+b$, then $y'= a b y^2 - a y$. Perhaps this helps.
$endgroup$
– lhf
Mar 12 at 0:16












$begingroup$
How good is that , differentiation of $n$ times of this will yield its n-th derivative in terms of n-1th or less.
$endgroup$
– M Desmond
Mar 12 at 15:20





$begingroup$
How good is that , differentiation of $n$ times of this will yield its n-th derivative in terms of n-1th or less.
$endgroup$
– M Desmond
Mar 12 at 15:20













$begingroup$
For $cot x$, see math.stackexchange.com/questions/1701540/…
$endgroup$
– lhf
2 days ago





$begingroup$
For $cot x$, see math.stackexchange.com/questions/1701540/…
$endgroup$
– lhf
2 days ago











1 Answer
1






active

oldest

votes


















4












$begingroup$

$$dfracd^ndx^n f(x) = fraca^n P_n(e^ax)(e^ax+b)^n+1$$
where $P_n$ is a polynomial of degree $n$, with
$P_0(t) = 1$ and
$$ P_n+1(t) = t (b + t) P_n'(t) - (n+1) t P(t)$$
I don't think there's a "closed form", unless you count Faà_di_Bruno's formula






share|cite|improve this answer











$endgroup$












  • $begingroup$
    (+1)Thanks sir, can you recommend any references where i can find the proof of Faa di bruno's formula. I have never heard of this before.
    $endgroup$
    – M Desmond
    Mar 12 at 15:16










Your Answer





StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: true,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);













draft saved

draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3144103%2fis-it-possible-to-find-nth-derivative-of-frac1eaxb%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown

























1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes









4












$begingroup$

$$dfracd^ndx^n f(x) = fraca^n P_n(e^ax)(e^ax+b)^n+1$$
where $P_n$ is a polynomial of degree $n$, with
$P_0(t) = 1$ and
$$ P_n+1(t) = t (b + t) P_n'(t) - (n+1) t P(t)$$
I don't think there's a "closed form", unless you count Faà_di_Bruno's formula






share|cite|improve this answer











$endgroup$












  • $begingroup$
    (+1)Thanks sir, can you recommend any references where i can find the proof of Faa di bruno's formula. I have never heard of this before.
    $endgroup$
    – M Desmond
    Mar 12 at 15:16















4












$begingroup$

$$dfracd^ndx^n f(x) = fraca^n P_n(e^ax)(e^ax+b)^n+1$$
where $P_n$ is a polynomial of degree $n$, with
$P_0(t) = 1$ and
$$ P_n+1(t) = t (b + t) P_n'(t) - (n+1) t P(t)$$
I don't think there's a "closed form", unless you count Faà_di_Bruno's formula






share|cite|improve this answer











$endgroup$












  • $begingroup$
    (+1)Thanks sir, can you recommend any references where i can find the proof of Faa di bruno's formula. I have never heard of this before.
    $endgroup$
    – M Desmond
    Mar 12 at 15:16













4












4








4





$begingroup$

$$dfracd^ndx^n f(x) = fraca^n P_n(e^ax)(e^ax+b)^n+1$$
where $P_n$ is a polynomial of degree $n$, with
$P_0(t) = 1$ and
$$ P_n+1(t) = t (b + t) P_n'(t) - (n+1) t P(t)$$
I don't think there's a "closed form", unless you count Faà_di_Bruno's formula






share|cite|improve this answer











$endgroup$



$$dfracd^ndx^n f(x) = fraca^n P_n(e^ax)(e^ax+b)^n+1$$
where $P_n$ is a polynomial of degree $n$, with
$P_0(t) = 1$ and
$$ P_n+1(t) = t (b + t) P_n'(t) - (n+1) t P(t)$$
I don't think there's a "closed form", unless you count Faà_di_Bruno's formula







share|cite|improve this answer














share|cite|improve this answer



share|cite|improve this answer








edited Mar 11 at 19:54









user

5,35711030




5,35711030










answered Mar 11 at 19:47









Robert IsraelRobert Israel

327k23216470




327k23216470











  • $begingroup$
    (+1)Thanks sir, can you recommend any references where i can find the proof of Faa di bruno's formula. I have never heard of this before.
    $endgroup$
    – M Desmond
    Mar 12 at 15:16
















  • $begingroup$
    (+1)Thanks sir, can you recommend any references where i can find the proof of Faa di bruno's formula. I have never heard of this before.
    $endgroup$
    – M Desmond
    Mar 12 at 15:16















$begingroup$
(+1)Thanks sir, can you recommend any references where i can find the proof of Faa di bruno's formula. I have never heard of this before.
$endgroup$
– M Desmond
Mar 12 at 15:16




$begingroup$
(+1)Thanks sir, can you recommend any references where i can find the proof of Faa di bruno's formula. I have never heard of this before.
$endgroup$
– M Desmond
Mar 12 at 15:16

















draft saved

draft discarded
















































Thanks for contributing an answer to Mathematics Stack Exchange!


  • Please be sure to answer the question. Provide details and share your research!

But avoid …


  • Asking for help, clarification, or responding to other answers.

  • Making statements based on opinion; back them up with references or personal experience.

Use MathJax to format equations. MathJax reference.


To learn more, see our tips on writing great answers.




draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3144103%2fis-it-possible-to-find-nth-derivative-of-frac1eaxb%23new-answer', 'question_page');

);

Post as a guest















Required, but never shown





















































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown

































Required, but never shown














Required, but never shown












Required, but never shown







Required, but never shown







-

Popular posts from this blog

Moe incest case Sentencing See also References Navigation menu"'Australian Josef Fritzl' fathered four children by daughter""Small town recoils in horror at 'Australian Fritzl' incest case""Victorian rape allegations echo Fritzl case - Just In (Australian Broadcasting Corporation)""Incest father jailed for 22 years""'Australian Fritzl' sentenced to 22 years in prison for abusing daughter for three decades""RSJ v The Queen"

2009 crimes in AustraliaPeople convicted of incestRape in AustraliaChild abuse incidents and cases Victoria Police Moe, Victoria, Australiarapedphysically abusedviolencediedallegationsNews LimitedinvestigateMelbournedevelopmental problemsintellectually disabledspeech impedimentbirth certificateschargedsexual abuseDNA testspleadedguiltyincestindecent assaultcommon assaultsentencingimprisonmentparolesex offender registryappeal The Moe incest case emerged in February 2007 when a woman, identified as M for legal reasons, reported to Victoria Police in the town of Moe, Victoria, Australia that her 63-year-old father, RSJ, had raped, [1] [2] physically abused, and kept her a virtual prisoner in her own home between 1977 and 2005. Police had known about the alleged abuse since 2005, when M first came forward, but could not act because she did not want to cooperate after her father threatened violence against her mother and siblings. The J family had been known to authorities for more than ...
Read more

Do native speakers use “ultima” and “proxima” frequently in spoken English?How do native speakers say 'the light bulb has stopped working'the difference between “to revamp” ,“enhance” and “overhaul”How do we tell our currently running year of age?What's the layperson's term for words like “am”, “be”, “were”?How do I speak about a respectful person?Finger distance in musicWhat do we call English with dots and dashes?Do native speakers use 'so-so'?How to express “friends that I only know them on internet” English?Does “Until when” sound natural for native speakers?

Image
Is a roofing delivery truck likely to crack my driveway slab? Failed to fetch jessie backports repository How do I rename a LINUX host without needing to reboot for the rename to take effect? Told by Professor that this is PIE, but don't see how it's PIE. Help understanding what constitutes the sets, or alternative ways to solve? Can I Retrieve Email Addresses from BCC? Is it correct to write "is not focus on"? Why Were Madagascar and New Zealand Discovered So Late? How can I replace every global instance of "x[2]" with "x_2" How can a function with a hole (removable discontinuity) equal a function with no hole? Was Spock the First Vulcan in Starfleet? How was Earth single-handedly capable of creating 3 of the 4 gods of chaos? Short story about space worker geeks who zone out by 'listening' to radiation from stars (Bedrock Edition) Loading more than six chunks at once Why, precisely, is argon used in neutrino exper...
Read more

Who is our nearest planetary neighbor, on average?Santa Claus flies to the South PoleSeven Spheres of Unequal Mass, a weighing problem with a twistDescribe a large integerFast Mental Calculation of $7.5^7$Math in Space (without the help of celebrities)Find the value of $bigstar$: Puzzle 8 - InequalityWho drinks beer while running anyway?A Crucial DeliveryRanking And AverageHow long will my money last at roulette?

Image
How can I create URL shortcuts/redirects for task/diff IDs in Phabricator? What are the rules for concealing thieves' tools (or items in general)? Does convergence of polynomials imply that of its coefficients? Is xar preinstalled on macOS? Single word to change groups Triple Trouble Tribond label a part of commutative diagram What (if any) is the reason to buy in small local stores? TDE Master Key Rotation Do people actually use the word "kaputt" in conversation? If I cast the Enlarge/Reduce spell on an arrow, what weapon could it count as? How can a new country break out from a developed country without war? 10 year ban after applying for a UK student visa Do I need an EFI partition for each 18.04 ubuntu I have on my HD? Norwegian Refugee travel document Why do I have a large white artefact on the rendered image? Print a physical multiplication table Would it be believable to defy demographics in a story? Extraneous elements in "...
Read more