Jambmaths question:
If $y=x\cos x$find $\frac{dy}{dx}$
Option A:
$\cos x+x\sin x$
Option B:
$\cos x-x\cos x$
Option C:
$\sin x-x\cos x$
Option D:
$\sin x+x\cos x$
Jamb Maths Solution:
$\begin{align} & \text{Using the product rule} \\ & \frac{dy}{dx}=u\frac{dv}{dx}+v\frac{du}{dx} \\ & \frac{dy}{dx}=x\frac{d}{dx}(\cos x)+\cos x\frac{d}{dx}(x) \\ & \frac{dy}{dx}=x(-\sin x)+\cos x(1) \\ & \frac{dy}{dx}=-x\sin x+\cos x \\ & \frac{dy}{dx}=\cos x-x\sin x \\\end{align}$
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