Chapter 6.4, Problem 7QR

To determine

To find $dy/dx$ .

Answer to Problem 7QR

  $\frac{dy}{dx}=\frac{-x\sin x-\cos x}{x^2}$

Explanation of Solution

Given: Function is

  $y=\frac{\cos x}{x}$

Calculation:

  $y=\frac{\cos x}{x}$

Differentiate with respect to $x$

  $\begin{array}{l}\frac{dy}{dx}=\frac{d}{dx}\left[\frac{\cos x}{x}\right]\\ =\frac{x\frac{d}{dx}\left(\cos x\right)-\cos x\frac{d}{dx}\left(x\right)}{x^2}\\ =\frac{-x\sin x-\cos x}{x^2}\end{array}$