Calculus Examples

$y = \frac{7}{3 x^{- 2}}$

Step 1

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

$\frac{d}{d x} [\frac{7 x^{2}}{3}]$

Step 2

Since $\frac{7}{3}$ is constant with respect to $x$ , the derivative of $\frac{7 x^{2}}{3}$ with respect to $x$ is $\frac{7}{3} \frac{d}{d x} [x^{2}]$ .

$\frac{7}{3} \frac{d}{d x} [x^{2}]$

Step 3

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

$\frac{7}{3} (2 x)$

Step 4

Combine fractions.

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Step 4.1

Combine $2$ and $\frac{7}{3}$ .

$\frac{2 \cdot 7}{3} x$

Step 4.2

Multiply $2$ by $7$ .

$\frac{14}{3} x$

Step 4.3

Combine $\frac{14}{3}$ and $x$ .

$\frac{14 x}{3}$