Compute the derivative of f(x) = sin2 x.

Question

Compute the derivative of f(x) = sin2 x. (A) sin 2x (B) 2 sin x (C) 2x sin 2x (D) sin x

Tardigrade Admin · Accepted Answer

We have, f(x) = sin2 x ∴ (d/dx)[f(x)]=(d/dx)(sin x sin x) (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

Q. Compute the derivative of $f (x) = s i n^{2} x$ .

$s in 2 x$

$2 s in x$

$2 x s in 2 x$

$s in x$

We have, $f (x) = s i n^{2} x$
$∴ \frac{d}{d x} [f (x)] = \frac{d}{d x} (s in x s in x)$ (Using product rule)
$= (s in x)^{'} s in x + s in x (s in x)^{'}$
$= (cos x) s in x + s in x (cos x)$
$= 2 s in x cos x = s in 2 x$

Q. Compute the derivative of f(x)=sin2x.

sin2x

2sinx

2xsin2x

sinx