Chapter 4.1, Problem 21E

To determine

To calculate:The differentiation of the given function.

Answer to Problem 21E

The differentiation is $3\sin (6x-4)$ .

Explanation of Solution

Given information: Given function is $y={\sin }^2(3x-2)$ .

Formula used: $\frac{d(x^n)}{dx}=n{x}^{n-1},\frac{d(\sin x)}{dx}=\cos x\text{and}\sin 2A=2\sin A\cos A$ with chain and subtraction rule.

Calculation:

  $y={\sin }^2(3x-2)$

Differentiate with respect to x :

  $\begin{array}{l}\frac{dy}{dx}=\frac{d[{\sin }^2(3x-2)]}{d[\sin (3x-2)]}\times \frac{d[\sin (3x-2)]}{d(3x-2)}\times \frac{d(3x-2)}{dx}\\ \frac{dy}{dx}=2\times \sin (3x-2)\times \cos (3x-2)\times 3\\ \frac{dy}{dx}=3\times \sin (6x-4)\end{array}$