Question

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

Answer 1

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

Solution.

Using chain rule:

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

Answer.

cos 2x