Find the Derivative – d/dr 2pirh+2pir^2

$2 π r h + 2 π r^{2}$

By the Sum Rule, the derivative of $2 π r h + 2 π r^{2}$ with respect to $r$ is $\frac{d}{d r} [2 π r h] + \frac{d}{d r} [2 π r^{2}]$ .

$\frac{d}{d r} [2 π r h] + \frac{d}{d r} [2 π r^{2}]$

Evaluate $\frac{d}{d r} [2 π r h]$ .

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Since $2 π h$ is constant with respect to $r$ , the derivative of $2 π r h$ with respect to $r$ is $2 π h \frac{d}{d r} [r]$ .

$2 π h \frac{d}{d r} [r] + \frac{d}{d r} [2 π r^{2}]$

Differentiate using the Power Rule which states that $\frac{d}{d r} [r^{n}]$ is $n r^{n - 1}$ where $n = 1$ .

$2 π h \cdot 1 + \frac{d}{d r} [2 π r^{2}]$

Multiply $2$ by $1$ .

$2 π h + \frac{d}{d r} [2 π r^{2}]$

Evaluate $\frac{d}{d r} [2 π r^{2}]$ .

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Since $2 π$ is constant with respect to $r$ , the derivative of $2 π r^{2}$ with respect to $r$ is $2 π \frac{d}{d r} [r^{2}]$ .

$2 π h + 2 π \frac{d}{d r} [r^{2}]$

Differentiate using the Power Rule which states that $\frac{d}{d r} [r^{n}]$ is $n r^{n - 1}$ where $n = 2$ .

$2 π h + 2 π (2 r)$

Multiply $2$ by $2$ .

$2 π h + 4 π r$

Find the Derivative – d/dr 2pirh+2pir^2

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