Calculus Examples

$\frac{4}{5 t}$

Step 1

Since $\frac{4}{5}$ is constant with respect to $t$ , the derivative of $\frac{4}{5 t}$ with respect to $t$ is $\frac{4}{5} \frac{d}{d t} [\frac{1}{t}]$ .

$\frac{4}{5} \frac{d}{d t} [\frac{1}{t}]$

Step 2

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

$\frac{4}{5} \frac{d}{d t} [t^{- 1}]$

Step 3

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

$\frac{4}{5} (- t^{- 2})$

Step 4

Combine fractions.

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Step 4.1

Combine $\frac{4}{5}$ and $t^{- 2}$ .

$- \frac{4 t^{- 2}}{5}$

Step 4.2

Move $t^{- 2}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$- \frac{4}{5 t^{2}}$