The derivative of f (x) = sin2 x is

Question

The derivative of f (x) = sin2 x is (A)  cos 2x (B)  tan 2x (C)  sin 2x (D) cosec 2x

Tardigrade Admin · Accepted Answer

We use the product rule to evaluate this (df(x)/dx) = (d/dx) ( sin x sin x) =( sin x) sin x+ sin( sin x) =( cos x) sin x+ sin( cos x) = 2 sin x cos x = sin 2x

Q. The derivative of $f (x) = sin^{2} x$ is

$cos 2 x$

$tan 2 x$

$sin 2 x$

$cosec 2 x$

We use the product rule to evaluate this $\frac{df ( x )}{d x}$
$= \frac{d}{d x} (sin x sin x)$
$= (sin x) sin x + sin (sin x)$
$= (cos x) sin x + sin (cos x)$
$= 2 sin x cos x = sin 2 x$

Q. The derivative of f(x)=sin2x is

cos2x

tan2x

sin2x

cosec2x