Derivative of $x^{2} + 1$

The calculator will find the derivative of

x^{2} + 1

, with steps shown.

Find $\frac{d}{dx} \left(x^{2} + 1\right)$ .

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

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

The derivative of a constant is $0$ :

2 x + {\color{red}\left(\frac{d}{dx} \left(1\right)\right)} = 2 x + {\color{red}\left(0\right)}

Thus, $\frac{d}{dx} \left(x^{2} + 1\right) = 2 x$ .

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

Derivative of x2+1x^{2} + 1x2+1