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

1 Answer
Cameron J.
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)= #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))#

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