Find the requested partial derivative.
-$( \partial w / \partial x ) _ { y , z }$ if $w = x ^ { 3 } + y ^ { 3 } + z ^ { 3 } + 9 x y z$
A) $3 \left( x ^ { 2 } + 3 y z \right)$
B) $3 \left( x ^ { 2 } + 3 x y z \right)$
C) $3 \left( x ^ { 2 } + 6 y z \right)$
D) $3 \left( x ^ { 2 } + 6 x y z \right)$

Question

Quizplus · Accepted Answer

To find $( \partial w / \partial x ) _ { y , z }$, differentiate $w = x ^ { 3 } + y ^ { 3 } + z ^ { 3 } + 9 x y z$ with respect to $x$, treating $y$ and $z$ as constants. The derivative of $x^3$ with respect to $x$ is $3x^2$, and the derivative of $9xyz$ with respect to $x$ is $9yz$. The terms $y^3$ and $z^3$ are treated as constants and their derivatives with respect to $x$ are zero. Therefore, the partial derivative is $3x^2 + 9yz = 3(x^2 + 3yz)$.

Find the Requested Partial Derivative (∂w/∂x)y,z( \partial w / \partial x ) _ { y , z }(∂w/∂x)y,z​

Find the Requested Partial Derivative $( \partial w / \partial x ) _ { y , z }$