Question

Find the derivative of the function. dy/dx=

y=(3x^2-6x+1)^3

Answer 1

Use the power rule first and then the chain rule

or

Let z = 3x^2-6x+1
Then y = z^3
dy/dx = (dy/dz)(dz/dx)

Answer 2

use the power rule which is: y = x^n then y' = n x^(n-1)
and chain rule...
y = (stuff)^3 then y' = 3(stuff)^(3-1) * deriv (stuff)

Answer 3

so y=(3x^2-6x+1)^3
y' = 3(3x^2-6x+1)^2 * deriv (3x^2-6x+1)
= 3(3x^2-6x+1)^2 * (6x - 6)
= 18(x - 1)(3x^2-6x+1)^2