Question

How do you use the chain rule to differentiate `y=sin^3(2x+1)`?

Answer 1

`(dy)/(dx) = 6sin^2(2x+1)cos(2x+1)`

Explanation:

`u(x) = 2x+1` so `(du)/(dx) = 2`

`y = sin^3(u) implies (dy)/(du) = 3sin^2(u)cos(u)`

`(dy)/(dx) = (dy)/(du)(du)/(dx)`

`(dy)/(dx) = 6sin^2(2x+1)cos(2x+1)`