# How do you use the chain rule to differentiate y=(x+1)^(1/2)?

Jul 31, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = \left(\frac{1}{2}\right) {\left(x + 1\right)}^{- \frac{1}{2}}$

#### Explanation:

First, we need to use the power rule to take the derivative of outside.

$\frac{\mathrm{dy}}{\mathrm{dx}} = \left(\frac{1}{2}\right) {\left(x + 1\right)}^{- \frac{1}{2}}$

Chain rule basically tells you to take the derivative of inside of the function. In this case, the derivative of (x+1) is just 1, which wouldn't make any changes to previous derivative.

$\frac{\mathrm{dy}}{\mathrm{dx}} = \left(\frac{1}{2}\right) {\left(x + 1\right)}^{- \frac{1}{2}} \cdot 1$