Question

How do you find the derivative of `y=2cosxsinx`

Answer 1

`2cos(2x)`

Explanation:

Since `y = 2 cos(x) sin(x)` is the same as
`y = sin (2x)`

and
`(d sin(theta))/(d theta) = cos( theta)`

Let `g(a) = sin(a)` and `h(b) = 2b`
(So `y = g(h(x))`)

By the chain rule:
`(d y)/(dx) = (d g(h(x)))/(d h(x)) * (d h(x))/(dx)`

`color(white)((dy)(dx))=(d(sin(2x)))/(d(2x)) * (d(2x))/(dx)`

`color(white)((dy)(dx))= cos(2x) * 2`
or
`color(white)((dy)(dx))= 2 cos(2x)`