Question

Can you please help me find the derivative of this?

Answer 1

Given the equation:

`V(h)=(R^2\pi)/(3H^2)(H^2h-2Hh^2+h^3)`

To find the derivative, keep the constants and solve the derivative of each term.

The derivative can be found by using the equations below:

`\begin{gathered} f(x)=x \\ f^(\prime)(x)=1 \\ \\ f(x)=x^n \\ f^(\prime)(x)=n*x^(n-1) \end{gathered}`

Then, let's solve the derivative:

`\begin{gathered} V(h)=(R^(2)\pi)/(3H^(2))(H^(2)h-2Hh^(2)+h^(3)) \\ V^(\prime)(h)=(R^(2)\pi)/(3H^(2))(H^2*1-2H*2h^(2-1)+3*h^(3-1) \\ V^(\prime)(h)=(R^2\pi)/(3H^2)(H^2-4Hh+3h^2) \end{gathered}`

Answer:

`V^(\prime)(h)=(R^(2)\pi)/(3H^(2))(H^2-4Hh+3h^2)`