Question

Compute the derivative of $f(x) = sin^2\, x$.

• A. $sin \,2x$
• B. $2 \,sin\, x$
• C. $2x \,sin\, 2x$
• D. $sin\,x$

Answer 1

Answer: (A)

We have, $f(x) = sin^2\, x$
$\therefore \frac{d}{dx}\left[f\left(x\right)\right]=\frac{d}{dx}\left(sin\,x\,sin\,x\right)$ (Using product rule)
$= (sin\, x)' sin \,x + sin\, x(sin \,x)'$
$= (cos\, x) sin\, x + sin\, x(cos\, x) $
$= 2sin\, x \,cos \,x = sin \,2x$