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+(b)/(v)+cv^4`

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

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

To give

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

Hence, the answer is

`(dy)/(dv)=ae^v-(b)/(v^2)+4cv^3`