Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y), where x = r^2 + s^2 and y = 8rs, find ∂^2z/(∂r ∂s).

Question

i dont know how to do the chain rule in the higher order partial derivative.

Answer 1

dXrs = d/ds ( 2*r + s^2 )

= 2*s

dYrs = d/ds 8s = 8

So then 2s+8