Calculus Examples

$V = s^{3}$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d s} (V) = \frac{d}{d s} (s^{3})$

Step 2

The derivative of $V$ with respect to $s$ is $V'$ .

$V'$

Step 3

Differentiate using the Power Rule which states that $\frac{d}{d s} [s^{n}]$ is $n s^{n - 1}$ where $n = 3$ .

$3 s^{2}$

Step 4

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

$V' = 3 s^{2}$

Step 5

Replace $V'$ with $\frac{d V}{d s}$ .

$\frac{d V}{d s} = 3 s^{2}$