Find the derivative of $\dfrac{cos x}{x^2}$

The correct answer is $\dfrac{-(xsin x + 2cos x)}{x^3}$

As per Quotient Rule,

$\dfrac{dy}{dx}$ = $\dfrac{v \dfrac{du}{dx} - u \dfrac{dv}{dx}}{v^2}$


$ ∴ \dfrac{dy}{dx}$ = $\dfrac{x^2 D(cos x) - cos x D(x^2)}{x^4}$

= $\dfrac{x^2 (-sin x) - cos x (2x)}{x^4}$

= $ -x \dfrac{x (sin x) + cos x (2)}{x^4}$

= $\dfrac{-(xsin x + 2cos x)}{x^3}$