Solve v=1/3pi r^2 h

Evaluate

v = \frac{1}{3} π r^{2} h

Multiply the numbers

v = \frac{π}{3} r^{2} h

Find the first partial derivative by treating the variable h as a constant and differentiating with respect to r

\frac{\partial v}{\partial r} = \frac{\partial}{\partial r} (\frac{π}{3} r^{2} h)

Use differentiation rule \frac{\partial}{\partial x} (c f (x)) = c \times \frac{\partial}{\partial x} (f (x))

\frac{\partial v}{\partial r} = \frac{π}{3} h \times \frac{\partial}{\partial r} (r^{2})

Use \frac{\partial}{\partial x} x^{n} = n x^{n - 1} to find derivative

\frac{\partial v}{\partial r} = \frac{π}{3} h \times 2 r

Solution

\frac{\partial v}{\partial r} = \frac{2 π}{3} r h

Function