Find $f _ { x y }$ for the function $f ( x , y ) = 5 x ^ { 3 } y - 6 x y ^ { 2 }$ .
A) $f _ { x y } = 15 x ^ { 2 } + 12 y$
B) $f _ { x y } = 15 x ^ { 2 } - 12 y$
C) $f _ { x y } = 24 x ^ { 2 } - 12 y$
D) $f _ { x y } = 12 x ^ { 2 } - 15 y$
E) $f _ { x y } = 12 x ^ { 2 } + 15 y$

Question

Quizplus · Accepted Answer

To find $f_{xy}$, we differentiate $f_x$ with respect to y. First, we calculate $f_x$:
$$f_x=15x^2y-6y^2$$
Now we differentiate it with respect to y:
$$\frac{\partial}{\partial y}f_x=15x^2-12y$$
So, $f_{xy}=15x^2-12y$. Therefore, the answer is B.

Find fxyf _ { x y }fxy​ For the Function f(x,y)=5x3y−6xy2f ( x , y ) = 5 x ^ { 3 } y - 6 x y ^ { 2 }f(x,y)=5x3y−6xy2

Find $f _ { x y }$ For the Function $f ( x , y ) = 5 x ^ { 3 } y - 6 x y ^ { 2 }$