What is (\partial)/(\partial h)(4/3 pir^2h) ?

The answer to (\partial)/(\partial h)(4/3 pir^2h) is (4pir^2)/3

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(\partial)/(\partial h)(4/3 pir^2h)

\frac{\partial}{\partial h} (\frac{4}{3} π r^{2} h)

\frac{4 π r ^{2}}{3}

Solution steps

\frac{\partial}{\partial h} (\frac{4}{3} π r^{2} h)

Treat

r

as a constant

Take the constant out:

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

= \frac{4}{3} π r^{2} \frac{\partial}{\partial h} (h)

Apply the common derivative:

\frac{\partial}{\partial h} (h) = 1

= \frac{4}{3} π r^{2} \cdot 1

Simplify

\frac{4}{3} π r^{2} \cdot 1 : \frac{4 π r ^{2}}{3}

= \frac{4 π r ^{2}}{3}

What is (\partial)/(\partial h)(4/3 pir^2h) ?
The answer to (\partial)/(\partial h)(4/3 pir^2h) is (4pir^2)/3