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

The calculator will find the derivative of $$$x^{2} + 1$$$, with steps shown.

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Your Input

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

Solution

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

Answer

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