How do you differentiate (x+1)/2?

Jul 23, 2016

$\frac{1}{2}$

Explanation:

First rewrite the expression as follows.

$\frac{x + 1}{2} = \frac{1}{2} \left(x + 1\right) = \frac{1}{2} x + \frac{1}{2}$

now differentiate using the $\textcolor{b l u e}{\text{power rule}}$

$\textcolor{red}{| \overline{\underline{\textcolor{w h i t e}{\frac{a}{a}} \textcolor{b l a c k}{\frac{d}{\mathrm{dx}} \left(a {x}^{n}\right) = n a {x}^{n - 1} \text{ and " d/dx"(constant)} = 0} \textcolor{w h i t e}{\frac{a}{a}} |}}}$

$\frac{d}{\mathrm{dx}} \left(\frac{1}{2} x + \frac{1}{2}\right) = \frac{1}{2} + 0 = \frac{1}{2}$