Question

Find derivative of the function:

y = (4x+1)^2 (1-x)^3

Answer 1

use the product rule and the chain rule:
y = u^2 v^3
y' = 2u u' * v^3 + u^2 + 3v^2 v'
= uv^2 (2vu' + 3uv')
= (4x+1)(1-x)^2 (2(1-x)(4) + 3(4x+1)(-1))
= 5(4x+1)(1-x)^2 (1-4x)
= -5(16x^2-1)(1-x)^2