Calculus Examples

$a = p r^{2}$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d r} (a) = \frac{d}{d r} (p r^{2})$

Step 2

The derivative of $a$ with respect to $r$ is $a'$ .

$a'$

Step 3

Differentiate the right side of the equation.

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Step 3.1

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

$p \frac{d}{d r} [r^{2}]$

Step 3.2

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

$p (2 r)$

Step 3.3

Move $2$ to the left of $p$ .

$2 p r$

Step 4

Reform the equation by setting the left side equal to the right side.

$a' = 2 p r$

Step 5

Replace $a'$ with $\frac{d a}{d r}$ .

$\frac{d a}{d r} = 2 p r$