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Why 2 dimensional gradient's partial derivative determines direction in xy plane

Why is gradient the direction of steepest ascent?Why is gradient the direction of steepest ascent?Why partial derivations of scalar-valued function put into vector give direction of maximum increase?Direction of unit vector that maximize directional derivativeWhy in a directional derivative it has to be a unit vectorWhy the gradient vector gives the direction of maximum increase of a function?Direction of gradient vector in terms of partialWhy isn't the directional derivative generally scaled down to the unit vector?Why is any arbitrary directional derivative always recoverable from the gradient?What is intuition behind direction of derivative of a function?Directional derivative confusion - why does independently evaluating partial changes, then adding them, work?

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I was reading about gradient and I still can grasp why the components of the gradient are partial derivative. To be more precise, let say for a 2 dimensional function that for the point (5,3) my gradient is [2,1] from my understanding of partial derivative the i component in my gradient means that for every x unit my function increasea 2. What I don't understand is why moving 2 units in the x coodinate and then 1 unit in y coordinate give me the direction of greater increase. I can't relate how the partial derivative which in this example gives me the resulting change of moving in x and y direction using that resulting change in the function as a coordinate in the plane give me the right direction. Hope I am being clear. Probably I am interpreting something wrong

calculus derivatives

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asked Mar 22 at 2:08

kprincipekprincipe

998

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  See math.stackexchange.com/questions/223252/… and other related questions in the handy list at right.
  $endgroup$
  – amd
  Mar 22 at 3:56
  
  

  
  
  
  

add a comment | 

0

$begingroup$

I was reading about gradient and I still can grasp why the components of the gradient are partial derivative. To be more precise, let say for a 2 dimensional function that for the point (5,3) my gradient is [2,1] from my understanding of partial derivative the i component in my gradient means that for every x unit my function increasea 2. What I don't understand is why moving 2 units in the x coodinate and then 1 unit in y coordinate give me the direction of greater increase. I can't relate how the partial derivative which in this example gives me the resulting change of moving in x and y direction using that resulting change in the function as a coordinate in the plane give me the right direction. Hope I am being clear. Probably I am interpreting something wrong

calculus derivatives

share|cite|improve this question

asked Mar 22 at 2:08

kprincipekprincipe

998

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  See math.stackexchange.com/questions/223252/… and other related questions in the handy list at right.
  $endgroup$
  – amd
  Mar 22 at 3:56
  
  

  
  
  
  

add a comment | 

$begingroup$

I was reading about gradient and I still can grasp why the components of the gradient are partial derivative. To be more precise, let say for a 2 dimensional function that for the point (5,3) my gradient is [2,1] from my understanding of partial derivative the i component in my gradient means that for every x unit my function increasea 2. What I don't understand is why moving 2 units in the x coodinate and then 1 unit in y coordinate give me the direction of greater increase. I can't relate how the partial derivative which in this example gives me the resulting change of moving in x and y direction using that resulting change in the function as a coordinate in the plane give me the right direction. Hope I am being clear. Probably I am interpreting something wrong

calculus derivatives

share|cite|improve this question

asked Mar 22 at 2:08

kprincipekprincipe

998

$endgroup$

share|cite|improve this question

asked Mar 22 at 2:08

kprincipekprincipe

998

share|cite|improve this question

asked Mar 22 at 2:08

kprincipekprincipe

998

asked Mar 22 at 2:08

kprincipekprincipe

998

asked Mar 22 at 2:08

kprincipekprincipe

998