Question

Find \(\rm \frac {d^2 \cos 2x}{dx^2}\)
1. 4 sin 2x
2. -4 sin 2x
3. -4 cos 2x
4. 4 cos 2x

Answer 1

Correct Answer - Option 3 : -4 cos 2x

Concept:

Second-order Derivative.

\(\rm \frac {d^2 f(x)}{dx^2} = \) \(\rm \frac {d}{dx} [\frac {d}{dx} f(x)]\)

\( \rm \frac {d}{dx} \cos x = -\sin x\)

\( \rm \frac {d}{dx} \sin x = \cos x\)

Calculations:

Given:

 \(\rm \dfrac {d^2 \cos2x}{dx^2}\)

= \(\rm \dfrac {d}{dx} (\dfrac {d}{dx} cos2x)\)

=   \(\rm \dfrac {d}{dx} (- 2sin2x)\)

=  \(\rm -2\;\dfrac {d}{dx} ( sin2x)\)

=  -2 × 2 cos 2x

= -4 cos 2x