Find the Derivative - d/dt (ds)/(dt)

$\frac{d s}{d t}$

Step 1

Cancel the common factor of $d$ .

Cancel the common factor.

$\frac{d}{d t} [\frac{d s}{d t}]$

Rewrite the expression.

$\frac{d}{d t} [\frac{s}{t}]$

Step 2

Since $s$ is constant with respect to $t$ , the derivative of $\frac{s}{t}$ with respect to $t$ is $s \frac{d}{d t} [\frac{1}{t}]$ .

$s \frac{d}{d t} [\frac{1}{t}]$

Step 3

Rewrite $\frac{1}{t}$ as $t^{- 1}$ .

$s \frac{d}{d t} [t^{- 1}]$

Step 4

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

$s (- t^{- 2})$

Step 5

Simplify.

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$s (- \frac{1}{t^{2}})$

Combine $s$ and $\frac{1}{t^{2}}$ .

$- \frac{s}{t^{2}}$