Compute $f _ { x }$ for $f ( x , y ) = e ^ { 8 x y }$
A) $8 x y e ^ { 8 x y }$
B) $8 y e ^ { 8 x }$
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. The derivative of $e^{8xy}$ with respect to $x$ is $8y e^{8xy}$, because we treat $y$ as a constant and multiply by the derivative of the exponent $8xy$ with respect to $x$, which is $8y$. Therefore, the correct answer is $8y e^{8xy}$, but there seems to be a mistake in the options provided. Based on the correct calculation, none of the options accurately reflect $8y e^{8xy}$. There might be a typographical error in the choices or my response.

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

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