Calculus Examples

$y = \frac{3}{{(2 x)}^{- 2}}$

Step 1

This derivative could not be completed using the chain rule. Mathway will use another method.

Step 2

Factor $2$ out of $2 x$ .

$\frac{d}{d x} [\frac{3}{{(2 (x))}^{- 2}}]$

Step 3

Apply the product rule to $2 (x)$ .

$\frac{d}{d x} [\frac{3}{2^{- 2} x^{- 2}}]$

Step 4

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

$\frac{d}{d x} [\frac{3}{\frac{1}{2^{2}} x^{- 2}}]$

Step 5

Raise $2$ to the power of $2$ .

$\frac{d}{d x} [\frac{3}{\frac{1}{4} x^{- 2}}]$

Step 6

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

$\frac{d}{d x} [\frac{3 x^{2}}{\frac{1}{4}}]$

Step 7

Multiply by the reciprocal of the fraction to divide by $\frac{1}{4}$ .

$\frac{d}{d x} [3 x^{2} \cdot 4]$

Step 8

Multiply $4$ by $3$ .

$\frac{d}{d x} [12 x^{2}]$

Step 9

Since $12$ is constant with respect to $x$ , the derivative of $12 x^{2}$ with respect to $x$ is $12 \frac{d}{d x} [x^{2}]$ .

$12 \frac{d}{d x} [x^{2}]$

Step 10

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

$12 (2 x)$

Step 11

Multiply $2$ by $12$ .

$24 x$