(17) Differentiate the function in two ways. f(x) = (3x^2+3x-1)^2 (a) Use the general power rule. (b) Multiply 3x^2 + 3x - 1 by itself and then differentiate the resulting polynomial.

Question

(a) Rewrite​ f(x) using the general power rule.

f ' (x) _____ • d/dx [ ______ ]

Answer 1

(a) Power Rule and Chain Rule

Let u=3x²+3x-1

f(x)=u² and f'(x)= 2u (du/dx)=2(3x²+3x-1)(6x+3)=36x³+54x²+6x-6

(b) Differentiate polynomial

f(x)= (3x²+3x-1)² = (3x²+3x-1)(3x²+3x-1) = 9x⁴+18x³+3x²-6x+1

So f'(x) = 36x³+54x²+6x-6

You can factor a 6 out if you like