Calculus Examples

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

Step 1

Since $\frac{3}{\ln (2)}$ is constant with respect to $x$ , the derivative of $\frac{3}{x \ln (2)}$ with respect to $x$ is $\frac{3}{\ln (2)} \frac{d}{d x} [\frac{1}{x}]$ .

$\frac{3}{\ln (2)} \frac{d}{d x} [\frac{1}{x}]$

Step 2

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

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

Step 3

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

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

Step 4

Combine fractions.

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Step 4.1

Combine $\frac{3}{\ln (2)}$ and $x^{- 2}$ .

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

Step 4.2

Simplify the expression.

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Step 4.2.1

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

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

Step 4.2.2

Reorder factors in $- \frac{3}{\ln (2) x^{2}}$ .

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