Given the function
[tex]y=ae^v+\frac{b}{v}+cv^4[/tex]
To differentiate the function with respect to v, i.e dy/dv
[tex]\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}[/tex]
To give
[tex]\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}[/tex]
Hence, the answer is
[tex]\frac{dy}{dv}=ae^v-\frac{b}{v^2}+4cv^3[/tex]
