Question

How do you find the derivative of `sin2x - cos2x`?

Answer 1

2cos2x + 2sin2x

Explanation:

differentiate using`color(blue)" chain rule "`

`d/dx [ f(g(x)) ] = f'(g(x)). g'(x)`

apply this rule to each term

`d/dx(sin2x) = cos2x d/dx(2x) = 2cos2x`

`d/dx(cos2x) = -sin2x d/dx(2x) = -2sin2x`

`rArrd/dx(sin2x-cos2x) = 2cos2x + 2sin2x`