Thread: First-Order Partial Derivatives

Calculate the first-order partial derivative of the following:



for all (x,y) in

I used this as a composition function and used the chain rule.


However, I am unsure of how to apply this formula.

First-order partial derivative of x would be


First-order pairtal derivative of y would be


My question is : how to compute this? Do I do another composition+chain rule?

Thank you.

Originally Posted by Paperwings

Calculate the first-order partial derivative of the following:



for all (x,y) in

I used this as a composition function and used the chain rule.


However, I am unsure of how to apply this formula.

First-order partial derivative of x would be


First-order pairtal derivative of y would be


My question is : how to compute this? Do I do another composition+chain rule?

Thank you.

You cannot, it doesn't tell you what the function is. You have gone as far as you can


This is analgous to saying


.

Since in terms of the derivative in respect to x we don't care whether or not there are y's in there, this is just a normal chain rule of a function of x with some constants.

One more question: suppose that g has second derivative, how would I calculate the second partial derivatives of the function?

Hello,

Originally Posted by Paperwings

One more question: suppose that g has second derivative, how would I calculate the second partial derivatives of the function?

It depends on what second partial derivative you want.



You'll get the first one by taking the partial derivative of df/dx with respect to y. You'll get the second one by taking the partial derivative of df/dx with respect to x.

My book doesn't specify, but I'm pretty sure I'm supposed to find and . Thank you, Moo.

Originally Posted by Paperwings

My book doesn't specify, but I'm pretty sure I'm supposed to find and . Thank you, Moo.

Well then do what you did again

for just hold y constant again and use either the chain rule and product rule or a combination of both if waranted. Same thing with [tex]f_{yy}[/math ] except now x is the variable held as a constant. if it is indeed note that if hte curve is continuous that so you would only need to compute one.