Respuesta :

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]

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