Derivative of $$$u^{2} + 1$$$
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Your Input
Find $$$\frac{d}{du} \left(u^{2} + 1\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{du} \left(u^{2} + 1\right)\right)} = {\color{red}\left(\frac{d}{du} \left(u^{2}\right) + \frac{d}{du} \left(1\right)\right)}$$Apply the power rule $$$\frac{d}{du} \left(u^{n}\right) = n u^{n - 1}$$$ with $$$n = 2$$$:
$${\color{red}\left(\frac{d}{du} \left(u^{2}\right)\right)} + \frac{d}{du} \left(1\right) = {\color{red}\left(2 u\right)} + \frac{d}{du} \left(1\right)$$The derivative of a constant is $$$0$$$:
$$2 u + {\color{red}\left(\frac{d}{du} \left(1\right)\right)} = 2 u + {\color{red}\left(0\right)}$$Thus, $$$\frac{d}{du} \left(u^{2} + 1\right) = 2 u$$$.
Answer
$$$\frac{d}{du} \left(u^{2} + 1\right) = 2 u$$$A