Question

I need help on this calc question, differentiate the following function with respect to v. A and b are constants

Answer 1

Given the function

$y=ae^v+\frac{b}{v}+cv^4$

To differentiate the function with respect to v, i.e dy/dv

$\begin{gathered} y=ae^v+\frac{b}{v}+cv^4 \\ \frac{dy}{dv}=1(ae^v)+(-1)(bv^{-1-1})+4cv^{4-1} \end{gathered}$

To give

$\begin{gathered} \frac{dy}{dv}=1(ae^v)+(-1)(bv^{-1-1})+4cv^{4-1} \\ \frac{dy}{dv}=ae^v+(-1)(bv^{-2})+4cv^3 \\ \frac{dy}{dv}=ae^v-\frac{b}{v^2}+4cv^3 \end{gathered}$

Hence, the answer is

$\frac{dy}{dv}=ae^v-\frac{b}{v^2}+4cv^3$