Find the indicated derivative.
-Find $f_{y} f(x, y, z)=5 x^{5} e^{\left(2 y^{6}+3 z^{4}\right)}$
A) $60 x^{5} y^{5} e^{\left(2 y^{6}+3 z^{4}\right)}$
B) $60 x^{5} y^{5} e^{12 y^{5}}$
C) $12 y^{5} e^{2} y^{6}$
D) $12 y^{5} e^{\left(2 y^{6}+3 z^{4}\right)}$

Question

Quizplus · Accepted Answer

The partial derivative of $f$ with respect to $y$ involves differentiating the exponential term $e^{(2y^6 + 3z^4)}$ with respect to $y$. The derivative of $2y^6$ with respect to $y$ is $12y^5$, so the derivative is $5x^5 \cdot 12y^5 \cdot e^{(2y^6 + 3z^4)} = 60x^5y^5e^{(2y^6 + 3z^4)}$.

Find the Indicated Derivative fyf(x,y,z)=5x5e(2y6+3z4)f_{y} f(x, y, z)=5 x^{5} e^{\left(2 y^{6}+3 z^{4}\right)}fy​f(x,y,z)=5x5e(2y6+3z4)

Find the Indicated Derivative $f_{y} f(x, y, z)=5 x^{5} e^{\left(2 y^{6}+3 z^{4}\right)}$