Can anyone show me the steps to find the partial derivative of z with respect to u. I can't pinpoint my error.

$$z = (x-y) \div (x+y)$$
\[x = u \div v]
\[y = v^2 \div u]

Question

Can anyone show me the steps to find the partial derivative of z with respect to u. I can't pinpoint my error.

$$z = (x-y) \div (x+y)$$
\[x = u \div v]
\[y = v^2 \div u]

anonymous · Answer

$$y = v^2 \div u$$$$x = u \div v$$

anonymous · Answer

Draw a tree diagram.

anonymous · Answer

I am going to write the equation you should use, note I will use d for the partial symbol.  (dz/dx)*(dx/du) + (dz/dy)*(dy/du)

anonymous · Answer

Does this help any?

anonymous · Answer

Okay well I guess you don't need any more help.....

anonymous · Answer

I initially didn't pay too much attention to using the tree diagram but it does make steps more systematic and reduces the chances of stupid mistakes.

Thanks.