y = sin x cos x. Find the formula for dy. A) dy = -sin x cos x dx B) dy = (-sin ²x + cos ²x) dx C) dy = -sin ²(x + dx) + cos ²(x + dx) D) dy = (-sin ²(x + dx) + cos ²(x + dx)) - (-sin ² x + cos ²x) E) dy = sin (x +dx) cos (x +dx) - sin x cos x

Question

Quizplus · Accepted Answer

To find the derivative of $y = \sin x \cos x$, we use the product rule: $\frac{dy}{dx} = \sin x \cdot \frac{d}{dx}(\cos x) + \cos x \cdot \frac{d}{dx}(\sin x)$. This simplifies to $\frac{dy}{dx} = \sin x \cdot (-\sin x) + \cos x \cdot \cos x$, which further simplifies to $\frac{dy}{dx} = -\sin^2 x + \cos^2 x$. Therefore, $dy = (-\sin^2 x + \cos^2 x) dx$.

Y = Sin X Cos X