find the derivative of the function y=(2x+1)^3(4x+1)^-4

Answer 1

just use the product rule and chain rule:

y = uv
y' = u'v + uv'
where
u=(2x+1)^3
v=(4x+1)^-4

y' = 3(2x+1)^2(2)*(4x+1)^-4 + (2x+1)^3*(-4)(4x+1)^-5(4)
=

-2(2x+1)^2(4x+5)
---------------------
(4x+1)^5