Chapter 4.1, Problem 22E

To determine

To calculate:The differentiation of the given function.

Answer to Problem 22E

The differentiation is $-4\sin 2x(1+\cos 2x)$ .

Explanation of Solution

Given information: Given function is $y={(1+\cos 2x)}^2$ .

Formula used: $\frac{d(x^n)}{dx}=n{x}^{n-1}\text{and}\frac{d(\cos x)}{dx}=-\sin x$ with chain and addition rule.

Calculation:

  $y={(1+\cos 2x)}^2$

Differentiate with respect to x :

  $\begin{array}{l}\frac{dy}{dx}=\frac{d{(1+\cos 2x)}^2}{d(1+\cos 2x)}\times \frac{d(1+\cos 2x)}{dx}\\ \frac{dy}{dx}=2\times (1+\cos 2x)\times (-\sin 2x)\times 2\\ \frac{dy}{dx}=-4\times \sin 2x\times (1+\cos 2x)\end{array}$