Calculus Examples

$s = 7 \sin (t)$

Step 1

Differentiate both sides of the equation.

$\frac{d}{d t} (s) = \frac{d}{d t} (7 \sin (t))$

Step 2

The derivative of $s$ with respect to $t$ is $s'$ .

$s'$

Step 3

Differentiate the right side of the equation.

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Step 3.1

Since $7$ is constant with respect to $t$ , the derivative of $7 \sin (t)$ with respect to $t$ is $7 \frac{d}{d t} [\sin (t)]$ .

$7 \frac{d}{d t} [\sin (t)]$

Step 3.2

The derivative of $\sin (t)$ with respect to $t$ is $\cos (t)$ .

$7 \cos (t)$

Step 4

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

$s' = 7 \cos (t)$

Step 5

Replace $s'$ with $\frac{d s}{d t}$ .

$\frac{d s}{d t} = 7 \cos (t)$