partial derivatives of functions wrt to another function?

I came across this problem in a text I am using currently and was confused by the notation and am not sure of the answer

given a function

if and then is it correct to apply the pointwise vector coordinate function and get

This seemed like a trivial problem but the notation really confuses me.

Re: partial derivatives of functions wrt to another function?

Quote:

Originally Posted by

**knkumar** I came across this problem in a text I am using currently and was confused by the notation and am not sure of the answer

given a function

if

and

then is it correct to apply the pointwise vector coordinate function and get

This seemed like a trivial problem but the notation really confuses me.

Yes, that exactly what the notation means: . The fact that x, y, z are used as "place holders" in both functions is irrelevant.

This is exactly the same as if it were