Find the indicated derivative.
-Find $f_{x z} f(x, y, z)=5 x^{8} y^{5}+8 x^{6} z^{4}$
A) $4 z^{3}$
B) $32 x^{6} z^{3}$
C) $192 x^{5} z^{3}$
D) $40 x^{7} y^{5}+192 x^{5} z^{3}$

Question

Quizplus · Accepted Answer

First, find the partial derivative of $f$ with respect to $x$, then differentiate the result with respect to $z$. The derivative of $8x^6z^4$ with respect to $x$ is $48x^5z^4$, and differentiating this with respect to $z$ gives $192x^5z^3$.

Find the Indicated Derivative fxzf(x,y,z)=5x8y5+8x6z4f_{x z} f(x, y, z)=5 x^{8} y^{5}+8 x^{6} z^{4}fxz​f(x,y,z)=5x8y5+8x6z4

Find the Indicated Derivative $f_{x z} f(x, y, z)=5 x^{8} y^{5}+8 x^{6} z^{4}$