What is (\partial)/(\partial r)(pi/3 h^2(3r-h)) ?

The answer to (\partial)/(\partial r)(pi/3 h^2(3r-h)) is pih^2

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(\partial)/(\partial r)(pi/3 h^2(3r-h))

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

π h^{2}

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

\frac{\partial}{\partial r} (3 r) = 3

\frac{\partial}{\partial r} (h) = 0

= \frac{π}{3} h^{2} (3 - 0)

Simplify

\frac{π}{3} h^{2} (3 - 0) : π h^{2}

= π h^{2}

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What is (\partial)/(\partial r)(pi/3 h^2(3r-h)) ?
The answer to (\partial)/(\partial r)(pi/3 h^2(3r-h)) is pih^2