Question

Use the Chain Rule to find the indicated partial derivatives at p = 1, r = 2, and θ = 0 , given that
u = x4 + yz, x = pr sin(θ), y = pr cos(θ), and z = p + r .

Answer 1

\[u=x^4+yz\]\[x=pr\sin(\theta)\]\[y=pr\cos(\theta)\]\[z=p+r\]
\[\frac{\partial u}{\partial p}=\frac{\partial u}{\partial x}.\frac{\partial x}{\partial p}+\frac{\partial u}{\partial y}.\frac{\partial y}{\partial p}+\frac{\partial z}{\partial p}\]