Derivative of F(x) - (x^2 - x + 1)^3?

Question

show rules used and all working, for full points! !

Answer 1

I'm going to assume that your question has a typo in it and is actually f(x)=(x^2-x+1)^3.

Assuming this is true, then you begin by first noting that this problem involves the use of Chain Rule.

Using the Chain Rule, you take the derivative as you would normally, taking down the 3, subtracting 1 from the exponent, thus yielding 3(x^2-x+1)^2.

Following the chain rule further, you now take the derivative of the inner function, in this problem it is x^2-x+1. Taking the derivative of this yields 2x-1. Now in the final step of the Chain Rule, the answer to this problem is

3(x^2-x+1)^2 times 2x-1
Hope I helped!

Answer 2

f ( x ) = ( x ² - x + 1 ) ³
f `( x ) = 3 ( x ² - x + 1) ² ( 2x - 1)