Calculus Examples

$y = x G (x)$

Step 1

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

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

Step 2

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

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

Step 3

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

$\frac{d}{d x} [G x^{1 + 1}]$

Step 4

Add $1$ and $1$ .

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

Step 5

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

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

Step 6

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

$G (2 x)$

Step 7

Move $2$ to the left of $G$ .

$2 G x$