Question

How do you differentiate `y = sin 5x - 1/3 sin^3 5x`?

Answer 1

`color(brown)(y' = 5 cos (5x) (1 - sin^2 (5x))`

Explanation:

`y = sin 5x - (1/3) sin^3 (5x)`

`y' = (dy)/(dx) = cos 5x * 5 - (1/cancel3) cancel3 sin^2 (5x) cos 5x * 5`

`y' = 5 cos (5x) - 5 sin^2 (5x) * cos (5x)`

`y' = 5 cos (5x) (1 - sin^2 (5x))`