Calculus Examples

$\frac{1}{X^{3}}$

Step 1

Apply basic rules of exponents.

Tap for more steps...

Step 1.1

Rewrite $\frac{1}{X^{3}}$ as ${(X^{3})}^{- 1}$ .

$\frac{d}{d X} [{(X^{3})}^{- 1}]$

Step 1.2

Multiply the exponents in ${(X^{3})}^{- 1}$ .

Tap for more steps...

Step 1.2.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

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

Step 1.2.2

Multiply $3$ by $- 1$ .

$\frac{d}{d X} [X^{- 3}]$

Step 2

Differentiate using the Power Rule which states that $\frac{d}{d X} [X^{n}]$ is $n X^{n - 1}$ where $n = - 3$ .

$- 3 X^{- 4}$

Step 3

Simplify.

Tap for more steps...

Step 3.1

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

$- 3 \frac{1}{X^{4}}$

Step 3.2

Combine terms.

Tap for more steps...

Step 3.2.1

Combine $- 3$ and $\frac{1}{X^{4}}$ .

$\frac{- 3}{X^{4}}$

Step 3.2.2

Move the negative in front of the fraction.

$- \frac{3}{X^{4}}$