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

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

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

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

πh (2 r - h)

Solution steps

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

Treat

r

as a constant

Take the constant out:

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

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

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = h^{2}, g = 3 r - h

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

\frac{\partial}{\partial h} (h^{2}) = 2 h

\frac{\partial}{\partial h} (3 r - h) = - 1

= \frac{π}{3} (2 h (3 r - h) + (- 1) h^{2})

Simplify

\frac{π}{3} (2 h (3 r - h) + (- 1) h^{2}) : πh (2 r - h)

= πh (2 r - h)

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