$\text { For } f ( x , y ) = e ^ { y } \sin 11 x \text {, evaluate } f _ { y } \text { at the point } ( \pi , 0 ) \text {. }$
A) $f _ { y } ( \pi , 0 ) = 244$
B) $f _ { y } ( \pi , 0 ) = 23$
C) $f _ { y } ( \pi , 0 ) = 11$
D) $f _ { y } ( \pi , 0 ) = 22$
E) $f _ { y } ( \pi , 0 ) = 0$

Question

$\text { For } f ( x , y ) = e ^ { y } \sin 11 x \text {, evaluate } f _ { y } \text { at the point } ( \pi , 0 ) \text {. }$ 
A) $f _ { y } ( \pi , 0 ) = 244$
B) $f _ { y } ( \pi , 0 ) = 23$
C) $f _ { y } ( \pi , 0 ) = 11$
D) $f _ { y } ( \pi , 0 ) = 22$
E) $f _ { y } ( \pi , 0 ) = 0$

Quizplus · Accepted Answer

To find $f_y$, we differentiate $f(x, y) = e^y \sin 11x$ with respect to $y$, giving $f_y = e^y \sin 11x$. Evaluating at $(\pi, 0)$, we get $f_y(\pi, 0) = e^0 \sin 11\pi = 1 \cdot 0 = 0$, since $\sin$ of any integer multiple of $\pi$ is $0$.

For f(x,y)=eysin⁡11x, evaluate fy at the point (π,0). \text { For } f ( x , y ) = e ^ { y } \sin 11 x \text {, evaluate } f _ { y } \text { at the point } ( \pi , 0 ) \text {. } For f(x,y)=eysin11x, evaluate fy​ at the point (π,0).

$\text { For } f ( x , y ) = e ^ { y } \sin 11 x \text {, evaluate } f _ { y } \text { at the point } ( \pi , 0 ) \text {. }$