Find the second-order partial derivative.
-Find $\frac{\partial^{2} z}{\partial y^{2}}$ when $z=8 x e^{x y}$.
A) $8 x^{3} e^{x}$
B) $8 x^{3} e^{x y}$
C) $16 x^{2} e^{x y}$
D) $16 x^{2} e^{x}$

Question

Quizplus · Accepted Answer

First, find the first-order partial derivative with respect to $y$: $\frac{\partial z}{\partial y} = 8 x^2 e^{x y}$. Then, differentiate again with respect to $y$: $\frac{\partial^2 z}{\partial y^2} = 8 x^3 e^{x y}$.

Find the Second-Order Partial Derivative ∂2z∂y2\frac{\partial^{2} z}{\partial y^{2}}∂y2∂2z​ When z=8xexyz=8 x e^{x y}z=8xexy

Find the Second-Order Partial Derivative $\frac{\partial^{2} z}{\partial y^{2}}$ When $z=8 x e^{x y}$