Calculate $\frac { \partial f } { \partial x }$ , and $\frac { \partial f } { \partial y }$ when defined. $f ( x , y ) = e ^ { 2 x y }$
A) $\frac { \partial f } { \partial x } = 2 y e ^ { 2 x }$ , $\frac { \partial f } { \partial y } = 2 x e ^ { 2 y }$
B) $\frac { \partial f } { \partial x } = 2 y e ^ { 2 x y }$ , $\frac { \partial f } { \partial y } = 2 x e ^ { 2 x y }$
C) $\frac { \partial f } { \partial x } = e ^ { 2 x y }$ , $\frac { \partial f } { \partial y } = e ^ { 2 x y }$
D) $\frac { \partial f } { \partial x } = 2 e ^ { 2 x y }$ , $\frac { \partial f } { \partial y } = 2 e ^ { 2 x y }$
E) $\frac { \partial f } { \partial x } = 2 y$ , $\frac { \partial f } { \partial y } = 2 x$

Question

Calculate $\frac { \partial f } { \partial x }$ , and $\frac { \partial f } { \partial y }$ when defined.   $f ( x , y ) = e ^ { 2 x y }$  
A) $\frac { \partial f } { \partial x } = 2 y e ^ { 2 x }$ , $\frac { \partial f } { \partial y } = 2 x e ^ { 2 y }$
B) $\frac { \partial f } { \partial x } = 2 y e ^ { 2 x y }$ , $\frac { \partial f } { \partial y } = 2 x e ^ { 2 x y }$
C) $\frac { \partial f } { \partial x } = e ^ { 2 x y }$ , $\frac { \partial f } { \partial y } = e ^ { 2 x y }$
D) $\frac { \partial f } { \partial x } = 2 e ^ { 2 x y }$ , $\frac { \partial f } { \partial y } = 2 e ^ { 2 x y }$
E) $\frac { \partial f } { \partial x } = 2 y$ , $\frac { \partial f } { \partial y } = 2 x$

Quizplus · Accepted Answer

Using the chain rule, $\frac { \partial f } { \partial x } = 2y e^{2xy}$ because $2y$ is the derivative of the exponent $2xy$ with respect to $x$, and similarly, $\frac { \partial f } { \partial y } = 2x e^{2xy}$ because $2x$ is the derivative of the exponent $2xy$ with respect to $y$.

Calculate ∂f∂x\frac { \partial f } { \partial x }∂x∂f​ , And

Calculate $\frac { \partial f } { \partial x }$ , And