Question

Find the differentiation of $y$ w.r.t $x$ ,if $y=\frac{\sin x}{x}$

• A. $\frac{x\sin x-\cos x}{x^2}$
• B. $\frac{x\cos x-\sin x}{x}$
• C. $\frac{x\cos x-\sin x}{x^2}$
• D. $\frac{x^2\cos x-\sin x}{x^2}$

Answer 1

The correct option is C $\frac{x\cos x-\sin x}{x^2}$

Using quotient rule for differentiation,

If $f\left(x\right)=\sin x$, $g\left(x\right)=x$; then $f^{\prime }\left(x\right)=\cos x$ and $g^{\prime }\left(x\right)=1$
$⟹\frac{dy}{dx}=\frac{\left(\cos x\right)\left(x\right)-\left(\sin x\right)\left(1\right)}{x^2}=\frac{x\cos x-\sin x}{x^2}$