# Derivative of $x^{2} + 2 x$

The calculator will find the derivative of $x^{2} + 2 x$, with steps shown.

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

### Solution

The derivative of a sum/difference is the sum/difference of derivatives:

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

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 $f{\left(x \right)} = x$:

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

Apply the power rule $\frac{d}{dx} \left(x^{n}\right) = n x^{n - 1}$ with $n = 2$:

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

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

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

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

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