# Derivative of $2 x$

The calculator will find the derivative of $2 x$, with steps shown.

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Find $\frac{d}{dx} \left(2 x\right)$.

### Solution

Apply the constant multiple rule $\frac{d}{dx} \left(c f{\left(x \right)}\right) = c \frac{d}{dx} \left(f{\left(x \right)}\right)$ with $c = 2$ and $f{\left(x \right)} = x$:

$${\color{red}\left(\frac{d}{dx} \left(2 x\right)\right)} = {\color{red}\left(2 \frac{d}{dx} \left(x\right)\right)}$$

Apply the power rule $\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$ with $n = 1$, in other words, $\frac{d}{dx} \left(x\right) = 1$:

$$2 {\color{red}\left(\frac{d}{dx} \left(x\right)\right)} = 2 {\color{red}\left(1\right)}$$

Thus, $\frac{d}{dx} \left(2 x\right) = 2$.

$\frac{d}{dx} \left(2 x\right) = 2$A