Compute $f _ { x }$ for $f ( x , y ) = e ^ { 8 xy }$
A) $8 x y e ^ { 8 x y }$
B) $8 y e ^ { 8 x y }$
C) $8 x e ^ { 8 x y }$
D) $8 e ^ { 8 x y }$

Question

Quizplus · Accepted Answer

To compute $f_x$, the partial derivative of $f$ with respect to $x$, we apply the chain rule. Differentiating $e^{8xy}$ with respect to $x$ gives $8y e^{8xy}$ because the derivative of $8xy$ with respect to $x$ is $8y$, and then we multiply by the derivative of the exponential function, which is itself, resulting in $8y e^{8xy}$.

Compute fxf _ { x }fx​ For f(x,y)=e8xyf ( x , y ) = e ^ { 8 xy }f(x,y)=e8xy

Compute $f _ { x }$ For $f ( x , y ) = e ^ { 8 xy }$