Partial derivative, pls help !!

f(w,z)= w(w^2+z^2)^-1
Find f'w

Question

Partial derivative, pls help !!

f(w,z)= w(w^2+z^2)^-1
Find f'w

klimenkov · Answer

What is the biggest problem for you?

anonymous · Answer

I can't seem to get the answer

klimenkov · Answer

Do you know how to calculate the ordinary derivative, not the partial?

anonymous · Answer

Yes, for this question I use product rule, but just can't get the answer

klimenkov · Answer

Write here what you've got.

klimenkov · Answer

You can draw it using the "Draw" button.

anonymous · Answer

f'w = w X (-1)(w^2+z^2)^-2 X 2w + (w^2+z^2)^-1 (1)
       = -2w^3 (w^2+z^2) + (w^2+z^2)^-1

anonymous · Answer

= -2w^3 (w^2+z^2)^-2 + (w^2+z^2)^-1

klimenkov · Answer

You have to check the last answer very carefully. You are doing this right, but you are making mistakes. Check them.

anonymous · Answer

Which part is the mistake?

klimenkov · Answer

f'w = w X (-1)(w^2+z^2)^-2 X 2w + (w^2+z^2)^-1 - This is OK, but this
= -2w^3 (w^2+z^2) + (w^2+z^2)^-1 is not.
Try to find the common denominator in the first one and subtract the fractions.

anonymous · Answer

oh okay got it, thanks

klimenkov · Answer

You answered your question by yourself, I did not help you.