Compute $f _ { x }$ for $f ( x , y ) = e ^ { xy }$ .
A) $e ^ { x y }$
B) $x e ^ { x y }$
C) $y e ^ { xy }$
D) $x y e ^ { x y }$

Question

Quizplus · Accepted Answer

To compute $f_x$, the partial derivative of $f$ with respect to $x$, we apply the chain rule. Differentiating $e^{xy}$ with respect to $x$ gives $y e^{xy}$ because the derivative of $xy$ with respect to $x$ is $y$, and then we multiply by the derivative of the exponential function, which is itself, resulting in $y e^{xy}$.

Compute fxf _ { x }fx​ For f(x,y)=exyf ( x , y ) = e ^ { xy }f(x,y)=exy

Compute $f _ { x }$ For $f ( x , y ) = e ^ { xy }$