Derivative of $u^{2} + 1$

The calculator will find the derivative of

u^{2} + 1

, with steps shown.

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

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

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

The derivative of a constant is $0$ :

{\color{red}\left(\frac{d}{du} \left(1\right)\right)} + \frac{d}{du} \left(u^{2}\right) = {\color{red}\left(0\right)} + \frac{d}{du} \left(u^{2}\right)

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

{\color{red}\left(\frac{d}{du} \left(u^{2}\right)\right)} = {\color{red}\left(2 u\right)}

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

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

Derivative of u2+1u^{2} + 1u2+1