Question

Find the derivative of f(x) = (1 + 6x2)(x − x2) in two ways.

Answer 1

Using product rule;

f(x)=(1+6x²)(x-x²)

f'(x)=(12x)(x-x²) + (1-2x)(1+6x²) = 12x² -12x³ +1 +6x² -2x -12x³ = -24x³ +18x² -2x +1

Solving the bracket first;

f(x)=(1+6x²)(x-x²) = x -x² +6x³ -6x^4

f'(x)= 1 -2x +18x² -24x³ = -24x³ +18x² -2x +1