Question

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

Answer 1

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)= `sqrtg(x)`
then f'(x)= derivative of f with respect to g times derivative of g with respect to x, or
`(1/2*((x-1)(x-2)(x-3))^(-1/2))*d/dx((x-1)(x-2)(x-3))`

so the final answer is
f'(x) =`(3x^2−12x+11)/(2sqrt((x-1)(x-2)(x-3))`