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Derivative of $$$2 n - 1$$$
Related calculators: Logarithmic Differentiation Calculator, Implicit Differentiation Calculator with Steps
Your Input
Find $$$\frac{d}{dn} \left(2 n - 1\right)$$$.
Solution
The derivative of a sum/difference is the sum/difference of derivatives:
$${\color{red}\left(\frac{d}{dn} \left(2 n - 1\right)\right)} = {\color{red}\left(\frac{d}{dn} \left(2 n\right) - \frac{d}{dn} \left(1\right)\right)}$$The derivative of a constant is $$$0$$$:
$$- {\color{red}\left(\frac{d}{dn} \left(1\right)\right)} + \frac{d}{dn} \left(2 n\right) = - {\color{red}\left(0\right)} + \frac{d}{dn} \left(2 n\right)$$Apply the constant multiple rule $$$\frac{d}{dn} \left(c f{\left(n \right)}\right) = c \frac{d}{dn} \left(f{\left(n \right)}\right)$$$ with $$$c = 2$$$ and $$$f{\left(n \right)} = n$$$:
$${\color{red}\left(\frac{d}{dn} \left(2 n\right)\right)} = {\color{red}\left(2 \frac{d}{dn} \left(n\right)\right)}$$Apply the power rule $$$\frac{d}{dn} \left(n^{m}\right) = m n^{m - 1}$$$ with $$$m = 1$$$, in other words, $$$\frac{d}{dn} \left(n\right) = 1$$$:
$$2 {\color{red}\left(\frac{d}{dn} \left(n\right)\right)} = 2 {\color{red}\left(1\right)}$$Thus, $$$\frac{d}{dn} \left(2 n - 1\right) = 2$$$.
Answer
$$$\frac{d}{dn} \left(2 n - 1\right) = 2$$$A