Question

How do you differentiate `f(x)=2sinxcosx`?

Answer 1

`f'(x) = 2cos(2x)`

Explanation:

Use the identity `2sinthetacostheta = sin2theta` to rewrite the function.

`f(x) = sin2x`

Now, use the chain rule to differentiate.

Let `y = sinu` and `u = 2x`. `y' = cosu` and `u' = 2`.

`dy/dx = cosu xx 2 = cos(2x) xx 2 = 2cos(2x)`

Hopefully this helps!