Calculus Examples

$g (x) = x \log (2) x$

Step 1

Raise $x$ to the power of $1$ .

$\frac{d}{d x} [x^{1} x \log (2)]$

Step 2

Raise $x$ to the power of $1$ .

$\frac{d}{d x} [x^{1} x^{1} \log (2)]$

Step 3

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{d}{d x} [x^{1 + 1} \log (2)]$

Step 4

Add $1$ and $1$ .

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

Step 5

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

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

Step 6

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

$\log (2) (2 x)$

Step 7

Reorder.

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Step 7.1

Move $2$ to the left of $\log (2)$ .

$2 \cdot \log (2) x$

Step 7.2

Reorder the factors of $2 \log (2) x$ .

$2 x \log (2)$