Question

How do you differentiate # f(x) =2cosx+sin2x #?

Answer 1

`2cos(2x) -2sin(x)`

Explanation:

the derivative of `cos(x)` is defined as `-sin(x)`
therefore for the first term, the derivative of a constant multiplied by `cos(x)` gives that same constant multiplied by `-sin(x)`

therefore derivative of the first term is
`-2sin(x)`

the derivative of the second term can be found by using The Chain Rule

`d/dx f(g(x)) = f'(g(x))*g'(x)`

therefore,
let `f(x) = sin(x)`
and `g(x) = 2x`

therefore,
`d/dx f(g(x)) = d/dx sin(2x) = f'(g(x))*g'(x) = cos(2x)*2`

`= 2cos(2x)`

therefore, the entire derivative is,
`-2sin(x) + 2cos(2x)`
=