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Question

# Let$w = ( 4 x - 3 y + 2 z ) ^ { 5 }$. Find$\frac { \partial ^ { 2 } w } { \partial x \partial z }$

Solution

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We are given that

$w=(4x-3y+2z)^5$

We have to find $\dfrac{\partial }{\partial x}\left( \dfrac{\partial w}{\partial z} \right)$ So,

\begin{align*} w_{xz}&=\dfrac{\partial }{\partial x}\left( \dfrac{\partial }{\partial z}(4x-3y+2z)^5 \right) \\ &=\dfrac{\partial }{\partial x}\left( 10(4x-3y+2z)^4\right)\\ &=40(4x-3y+2z)^3(4)\\ &=160(4x-3y+2z)^3\\ \end{align*}

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