Question
Compute the derivative of f(x) = sin2 x.
✓
Answer
We have,
f(x) = sin2x
$\therefore \quad \frac { d f ( x ) } { d x } = \frac { d } { d x } ( \sin x \sin x )$
= (sin x)$ \frac { d } { d x } $sinx + sin x$ \frac { d } { d x } $(sinx) [using Leibnitz rule]
= (cos x)sinx + sinx(cos x)
= 2sin x cosx = sin 2x
f(x) = sin2x
$\therefore \quad \frac { d f ( x ) } { d x } = \frac { d } { d x } ( \sin x \sin x )$
= (sin x)$ \frac { d } { d x } $sinx + sin x$ \frac { d } { d x } $(sinx) [using Leibnitz rule]
= (cos x)sinx + sinx(cos x)
= 2sin x cosx = sin 2x
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