Answer to Question #313836 in Calculus for Jyo

Question

If (𝑥, 𝑦, 𝑧) =𝑋^ 2 𝑌 − 2 𝑌^ 2𝑍 ^3, find ∇𝑓 at the point (1, −1,2)

Answer 1

$\nabla f=\left( \frac{\partial f}{\partial x},\frac{\partial f}{\partial y},\frac{\partial f}{\partial z} \right) =\left( 2xy,x^2-4yz^3,-6y^2z^2 \right) \\ \nabla f(1,-1,2)=(-2,33,-24)$