Question

Given u(x, y) = x^2 + 2y where x (r, t) = r sin(t) and y(r,t) = sin^2(t), determine the value of ∂u / ∂r and ∂u / ∂t using the chain rule.

Plz show step

Answer 1

surely you know about the chain rule.

∂u/∂r = ∂u/∂x ∂x/∂r + ∂u/∂y ∂y/∂r
= 2x sin(t) + 2*0
= 2x sin(t)

similarly for ∂u/∂t

Answer 2

still dunno