Let f(x, y) = $x ^ { 3 }$ y + $e ^ { x + 3 y }$ . Compute $\frac { \partial ^ { 2 } \mathrm { f } } { \partial \mathrm { x } \partial \mathrm { y } }$ (1, 0).
A) 6
B) 3 + 3e
C) 6 + e
D) 3 + e
E) none of these

Question

Quizplus · Accepted Answer

First, compute the partial derivative of f with respect to x: $\frac{\partial f}{\partial x} = 3x^2y + e^{x+3y}$. Then, compute the partial derivative of this result with respect to y: $\frac{\partial^2 f}{\partial x \partial y} = 3x^2 + 3e^{x+3y}$. Evaluate at (1, 0): $3(1)^2 + 3e^{1+3(0)} = 3 + 3e$.

Let F(x, Y) = x3x ^ { 3 }x3 Y ex+3ye ^ { x + 3 y }ex+3y

Let F(x, Y) = $x ^ { 3 }$ Y $e ^ { x + 3 y }$