Question

Find the derivative of \( \sin^2 x \): \[ \frac{d}{dx} \left( \sin^2 x \right) \]

• A. \( 2\sin x \)
• B. \( \sin 2x \)
• C. \( \cos 2x \)
• D. \( 2\cos x \)

Hint:

To differentiate functions like \( \sin^2 x \), use the chain rule: \( \frac{d}{dx} \left( f(g(x)) \right) = f'(g(x)) \cdot g'(x) \). For \( \sin^2 x \), apply this to \( f(u) = u^2 \) and \( g(x) = \sin x \).

Answer 1

The Correct Option is D

We need to differentiate \( \sin^2 x \) with respect to \( x \). Using the chain rule: \[ \frac{d}{dx} \left( \sin^2 x \right) = 2 \sin x \cdot \cos x \] This simplifies to: \[ 2 \cos x \sin x \] which is the correct result. Therefore, the correct option is: \[ \boxed{2 \cos x} \]