Please help me with this!?

Question

What is the derivative of
f(x) = x(2x+1)^2 ?

Answer 1

f(x) = x(2x+1)^2

let g(x) = x and h(x) = (2x+1)² = 4x² + 4x + 1

f(x) = g(x) * h(x)

Using the product rule,

f'(x) = g(x) h'(x) + h(x) g'(x)

g'(x) = 8x + 4 and h'(x) = 1

Answer 2

f(x) = x(2x +1 )²
= x(4x² + 4x + 1)
= 4x³ + 4x² + x¹
f'(x) = 3∙4x³ˉ¹ + 2∙4x²ˉ¹ + 1∙x¹ˉ¹
= 12x² + 8x¹ + 1x⁰
= 12x² + 8x + 1