Thread: Question about taking a derivative

Im doing some online homework and I have a quick question. Take a look at the problem:

http://img412.imageshack.us/my.php?image=problemg.jpg

In order to calculate curl I know I take the cross product of the gradient and the function F. For the sake of discussion let us call the leading term of i-hat P, the leading term of j-hat Q, and the leading term of z-hat R.

You distribute that first term to each of the terms in the parenthesis. What would be the partial derivative of R with respect to y?

R = 6y/((x^2+y^2+z^2)^.5))

And when taking the partial derivative with respect to y you treat x and z as constants. So would i be correct in thinking that the partial derivative of R with respect to y would be 6? The derivative of a constant is always zero so can I just ignore the other x and z terms inside the square root sign?

I want to believe this because it would make this problem much easier, but something about doing that makes me uneasy and it seems mathematically incorrect to me. If this is not how you would do it would someone mind explaining me how to?

You treat them as constants, and if you say that , then you need to find the derivative of

So no, you can't ignore them in this case.