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