Question 36

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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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