Question

Find the first and second derivative for the function

g(t)=t^2(3t+1)^4

Answer 1

g' = (2t)(3t+1)^4 + (t^2)(4)(3t+1)^3 (3)
= 2t(9t+1)(3t+1)^3

g'' = 2(135t^2 + 30t + 1)(3t+1)^2