Compute $f _ { y }$ for $f ( x , y ) = 5 x y ^ { 3 }$
A) 5x
B) $15 x y ^ { 2 }$
C) $15 x y ^ { 2 } + 5 y ^ { 3 }$
D) $y ^ { 3 }$

Name: Compute $f _ { y }$ for $f ( x , y ) = 5 x y ^ { 3 }$ A) 5x B) $15 x y ^ { 2 }$ C) $15 x y ^ { 2 } + 5 y ^ { 3 }$ D) $y ^ { 3 }$
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Question

Quizplus · Accepted Answer

To find $f_y$, we differentiate $f(x, y) = 5xy^3$ with respect to $y$, treating $x$ as a constant. The derivative is $15xy^2$, which matches choice B.

Compute fyf _ { y }fy​ For f(x,y)=5xy3f ( x , y ) = 5 x y ^ { 3 }f(x,y)=5xy3

Compute $f _ { y }$ For $f ( x , y ) = 5 x y ^ { 3 }$