Find the following partial derivative: f_xy if $f ( x , y ) = x ^ { 7 } y ^ { 8 }$ . A) $f _ { x y } = 8 x ^ { 7 } y ^ { 7 }$ B) $f _ { x y } = 7 x ^ { 6 } y ^ { 8 }$ C) $f _ { x y } = 8 x ^ { 6 } y ^ { 7 }$ D) $f _ { x y } = 7 x ^ { 6 } y ^ { 7 }$ E) $f _ { x y } = 56 x ^ { 6 } y ^ { 7 }$

Question

Quizplus · Accepted Answer

The partial derivative of $f(x, y) = x^7y^8$ with respect to x and then y (or vice versa, since the order of differentiation does not matter for continuous functions) is $56x^6y^7$. This is found by first differentiating with respect to x to get $7x^6y^8$, and then differentiating that result with respect to y to get $56x^6y^7$.

Find the Following Partial Derivative: Fxy If f(x,y)=x7y8f ( x , y ) = x ^ { 7 } y ^ { 8 }f(x,y)=x7y8

Find the Following Partial Derivative: F_xy If $f ( x , y ) = x ^ { 7 } y ^ { 8 }$