JAMB Mathematics 2010 Paper

Concept:The function is a product of two simpler functions, so we apply the product rule of differentiation.Explanation:We are given $y = x \sin x$ and need $\frac{dy}{dx}$.Write the product as two functions: $u = x$ and $v = \sin x$.Differentiate each one with respect to $x$.The derivative of $x$ is $\frac{du}{dx} = 1$.The derivative of $\sin x$ is $\frac{dv}{dx} = \cos x$.The product rule states: $\frac{dy}{dx} = v\frac{du}{dx} + u\frac{dv}{dx}$.Now substitute $u$, $v$, $\frac{du}{dx}$, and $\frac{dv}{dx}$ into the formula.This gives $\frac{dy}{dx} = (\sin x)(1) + x(\cos x)$.Simplify the terms to obtain $\frac{dy}{dx} = \sin x + x\cos x$.This corresponds to option B.Answer:$\frac{dy}{dx} = \sin x + x\cos x$Thus, the correct option is B.