Question

Compute derivative of

(1) f(x) = sin 2x

Answer 1

Hi friend,

By using chain rule formula,

[f•g(x)] '= f'[(g(x)]. g'(x)

Given,

f(x)= sin(2x).

We know that the derivative of sin x is cos x.

Then

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

f'(x)= 2cos 2x.

This is the derivative of sin(2x).

Hope this helped you a little!!!

Answer 2

Hey !!

Let us recall the trigonometric formula

sin2x = 2 sinx cosx.

Thus,

  $\frac{df(x)}{dx} = \frac{d}{dx} (2sinx cosx) =2 \frac{d}{dx} (sinxcosx)$

     = $2 [ (sinx) cosx + sinx(cosx)]$

     = $2[(cosx)cosx + sinx(-sinx)]$

     = 2(cos²x - sin² x)

GOOD LUCK !!