Let $f ( x , y ) = x ^ { 2 } y ^ { 3 }$ . Find the value of the partial derivative $f _ { x } ( 1,1 )$ .
A)0
B)1
C)2
D)3
E)4
F)5
G)6
H)7

Question

Quizplus · Accepted Answer

To find the partial derivative of $f(x, y) = x^2y^3$ with respect to $x$, we treat $y$ as a constant and differentiate $x^2y^3$ with respect to $x$, which gives us $2xy^3$. Substituting $x = 1$ and $y = 1$ into $2xy^3$, we get $2 \cdot 1 \cdot 1^3 = 2$.

Let f(x,y)=x2y3f ( x , y ) = x ^ { 2 } y ^ { 3 }f(x,y)=x2y3

Let $f ( x , y ) = x ^ { 2 } y ^ { 3 }$