Give an appropriate answer.
-$f ( x , y ) = x ^ { 3 } - 7 x ^ { 2 } y - 6 x y ^ { 3 }$
A) $\frac { \partial f } { \partial x } = 3 x ^ { 2 } ; \frac { \partial f } { \partial y } = - 7 x ^ { 2 } - 18 x y ^ { 2 }$
B) $\frac { \partial f } { \partial x } = 3 x ^ { 2 } + 2 x y - 6 y ^ { 3 } ; \frac { \partial f } { \partial y } = - 7 x ^ { 2 } + 3 x y ^ { 2 }$
C) $\frac { \partial f } { \partial x } = 3 x ^ { 2 } - 14 x y - 6 y ^ { 3 } ; \frac { \partial f } { \partial y } = - 7 x ^ { 2 } - 18 x y ^ { 2 }$
D) $\frac { \partial f } { \partial x } = x ^ { 2 } - 7 x y - 6 y ^ { 3 } ; \frac { \partial f } { \partial y } = - 7 x ^ { 2 } - 6 x y ^ { 2 }$

Question

Quizplus · Accepted Answer

To find the partial derivatives of $f(x, y)$, we differentiate $f$ with respect to $x$ and $y$ separately. For $\frac{\partial f}{\partial x}$, we treat $y$ as a constant and differentiate each term with respect to $x$, resulting in $3x^2 - 14xy - 6y^3$. For $\frac{\partial f}{\partial y}$, we treat $x$ as a constant and differentiate each term with respect to $y$, resulting in $-7x^2 - 18xy^2$.

Give an Appropriate Answer f(x,y)=x3−7x2y−6xy3f ( x , y ) = x ^ { 3 } - 7 x ^ { 2 } y - 6 x y ^ { 3 }f(x,y)=x3−7x2y−6xy3

Give an Appropriate Answer $f ( x , y ) = x ^ { 3 } - 7 x ^ { 2 } y - 6 x y ^ { 3 }$