Given the equation:
[tex]V(h)=\frac{R^2\pi}{3H^2}(H^2h-2Hh^2+h^3)[/tex]
To find the derivative, keep the constants and solve the derivative of each term.
The derivative can be found by using the equations below:
[tex]\begin{gathered} f(x)=x \\ f^{\prime}(x)=1 \\ \\ f(x)=x^n \\ f^{\prime}(x)=n*x^{n-1} \end{gathered}[/tex]
Then, let's solve the derivative:
[tex]\begin{gathered} V(h)=\frac{R^{2}\pi}{3H^{2}}(H^{2}h-2Hh^{2}+h^{3}) \\ V^{\prime}(h)=\frac{R^{2}\pi}{3H^{2}}(H^2*1-2H*2h^{2-1}+3*h^{3-1} \\ V^{\prime}(h)=\frac{R^2\pi}{3H^2}(H^2-4Hh+3h^2) \end{gathered}[/tex]
Answer:
[tex]V^{\prime}(h)=\frac{R^{2}\pi}{3H^{2}}(H^2-4Hh+3h^2)[/tex]
