Calculus Examples

$- \frac{3}{t}$

Step 1

Since $- 3$ is constant with respect to $t$ , the derivative of $- \frac{3}{t}$ with respect to $t$ is $- 3 \frac{d}{d t} [\frac{1}{t}]$ .

$- 3 \frac{d}{d t} [\frac{1}{t}]$

Step 2

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

$- 3 \frac{d}{d t} [t^{- 1}]$

Step 3

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

$- 3 (- t^{- 2})$

Step 4

Multiply $- 1$ by $- 3$ .

$3 t^{- 2}$

Step 5

Simplify.

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Step 5.1

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

$3 \frac{1}{t^{2}}$

Step 5.2

Combine $3$ and $\frac{1}{t^{2}}$ .

$\frac{3}{t^{2}}$