Calculate $\frac { \partial f } { \partial x }$ and $\frac { \partial f } { \partial y }$ when defined.
$f ( x , y ) = 8 x ^ { 2 } y$
A) $\frac { \partial f } { \partial x } = 8 x ^ { 2 }$ , $\frac { \partial f } { \partial x } = 16 x y$
B) $\frac { \partial f } { \partial x } = 16 x$ , $\frac { \partial f } { \partial y } = 8 x y$
C) $\frac { \partial f } { \partial x } = 16 x y$ , $\frac { \partial f } { \partial y } = 8 x ^ { 2 }$
D) $\frac { \partial f } { \partial x } = 16 x y$ , $\frac { \partial f } { \partial y } = 8 x ^ { 2 } y$
E) $\frac { \partial f } { \partial x } = - 8 y ^ { 2 }$ , $\frac { \partial f } { \partial y } = - 16 x$

Question

Calculate $\frac { \partial f } { \partial x }$ and $\frac { \partial f } { \partial y }$ when defined.  
  $f ( x , y ) = 8 x ^ { 2 } y$  
A) $\frac { \partial f } { \partial x } = 8 x ^ { 2 }$ , $\frac { \partial f } { \partial x } = 16 x y$
B) $\frac { \partial f } { \partial x } = 16 x$ , $\frac { \partial f } { \partial y } = 8 x y$
C) $\frac { \partial f } { \partial x } = 16 x y$ , $\frac { \partial f } { \partial y } = 8 x ^ { 2 }$
D) $\frac { \partial f } { \partial x } = 16 x y$ , $\frac { \partial f } { \partial y } = 8 x ^ { 2 } y$
E) $\frac { \partial f } { \partial x } = - 8 y ^ { 2 }$ , $\frac { \partial f } { \partial y } = - 16 x$

Quizplus · Accepted Answer

To find $\frac { \partial f } { \partial x }$, treat $y$ as a constant and differentiate $f(x, y) = 8x^2y$ with respect to $x$, which gives $16xy$. To find $\frac { \partial f } { \partial y }$, treat $x$ as a constant and differentiate $f(x, y) = 8x^2y$ with respect to $y$, which gives $8x^2$.

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