Question

If y =cosx.sinx, differentiate with respect to x.

cos^2x−sin^2x
sin2x
cos^2x+sin^2x
cos2x

Answer 1

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Answer on Question # 47070 – Math – Differential Calculus | Equations

Task:

If $y = \cos x \sin x$, differentiate with respect to $x$.

A. $\cos^2 x - \sin^2 x$

B. $\sin 2x$

C. $\cos^2 x + \sin^2 x$

D. $\cos 2x$

Solution:

$$\frac{d}{dx} y = \frac{d}{dx} (\cos x \sin x) = \sin x \frac{d}{dx} (\cos x) + \cos x \frac{d}{dx} (\sin x) = - \sin^2 x + \cos^2 x = \cos (2x)$$

We applied differentiation rule for product of functions.

Thus, two answers ( A. $\cos^2 x - \sin^2 x$ and D. $\cos 2x$ ) are correct.