How do you differentiate f(x)=(2x^2-6x+1)^-8?

1 Answer
Oct 8, 2016

Use the chain rule. Please see explanation for details.

Explanation:

Use the chain rule (df(u(x)))/dx = ((df)/(du))((du)/dx)

let u(x) = 2x² - 6x + 1, then f(u) = u^(-8), (df(u))/(du) = -8u^(-9), and (du(x))/(dx) = 2x - 6

Substituting into the chain rule:

f'(x) = (-8u^(-9))(2x - 6)

Reverse the substitution for u:

f'(x) = -8(2x² - 6x + 1)^(-9)(2x - 6)

Simplify a bit:

f'(x) = (48 - 16x)/(2x² - 6x + 1)^(9)