Calculus Examples

$y = \frac{6}{5 x^{2}}$

Step 1

Since $\frac{6}{5}$ is constant with respect to $x$ , the derivative of $\frac{6}{5 x^{2}}$ with respect to $x$ is $\frac{6}{5} \frac{d}{d x} [\frac{1}{x^{2}}]$ .

$\frac{6}{5} \frac{d}{d x} [\frac{1}{x^{2}}]$

Step 2

Apply basic rules of exponents.

Tap for more steps...

Step 2.1

Rewrite $\frac{1}{x^{2}}$ as ${(x^{2})}^{- 1}$ .

$\frac{6}{5} \frac{d}{d x} [{(x^{2})}^{- 1}]$

Step 2.2

Multiply the exponents in ${(x^{2})}^{- 1}$ .

Tap for more steps...

Step 2.2.1

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

$\frac{6}{5} \frac{d}{d x} [x^{2 \cdot - 1}]$

Step 2.2.2

Multiply $2$ by $- 1$ .

$\frac{6}{5} \frac{d}{d x} [x^{- 2}]$

Step 3

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = - 2$ .

$\frac{6}{5} (- 2 x^{- 3})$

Step 4

Combine fractions.

Tap for more steps...

Step 4.1

Combine $- 2$ and $\frac{6}{5}$ .

$\frac{- 2 \cdot 6}{5} x^{- 3}$

Step 4.2

Multiply $- 2$ by $6$ .

$\frac{- 12}{5} x^{- 3}$

Step 4.3

Combine $\frac{- 12}{5}$ and $x^{- 3}$ .

$\frac{- 12 x^{- 3}}{5}$

Step 4.4

Simplify the expression.

Tap for more steps...

Step 4.4.1

Move $x^{- 3}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$\frac{- 12}{5 x^{3}}$

Step 4.4.2

Move the negative in front of the fraction.

$- \frac{12}{5 x^{3}}$