Solve v = pi*r^2*2h

Evaluate

v = π r^{2} \times 2 h

Use the commutative property to reorder the terms

v = 2 π 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} (2 π 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} = 2 πh \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} = 2 πh \times 2 r

Solution

\frac{\partial v}{\partial r} = 4 π r h

Function