# How do you differentiate y=sqrt( (x-1) (x-2) (x-3))?

Sep 2, 2016

Use the chain rule!

#### Explanation:

You have two functions here:
1. the square root function
2. a factored polynomial function

If we say g(x)=(x-1)(x-2)(x-3)
and f(x)= $\sqrt{g} \left(x\right)$
then f'(x)= derivative of f with respect to g times derivative of g with respect to x, or
$\left(\frac{1}{2} \cdot {\left(\left(x - 1\right) \left(x - 2\right) \left(x - 3\right)\right)}^{- \frac{1}{2}}\right) \cdot \frac{d}{\mathrm{dx}} \left(\left(x - 1\right) \left(x - 2\right) \left(x - 3\right)\right)$

f'(x) =(3x^2−12x+11)/(2sqrt((x-1)(x-2)(x-3))