Calculus Examples

$y = \frac{9}{u}$

Step 1

Since $9$ is constant with respect to $u$ , the derivative of $\frac{9}{u}$ with respect to $u$ is $9 \frac{d}{d u} [\frac{1}{u}]$ .

$9 \frac{d}{d u} [\frac{1}{u}]$

Step 2

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

$9 \frac{d}{d u} [u^{- 1}]$

Step 3

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

$9 (- u^{- 2})$

Step 4

Multiply $- 1$ by $9$ .

$- 9 u^{- 2}$

Step 5

Simplify.

Tap for more steps...

Step 5.1

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

$- 9 \frac{1}{u^{2}}$

Step 5.2

Combine terms.

Tap for more steps...

Step 5.2.1

Combine $- 9$ and $\frac{1}{u^{2}}$ .

$\frac{- 9}{u^{2}}$

Step 5.2.2

Move the negative in front of the fraction.

$- \frac{9}{u^{2}}$