Chapter 4.2, Problem 1QQ

To determine

To calculate: To find the $\frac{dy}{dx}$ of the function.

Answer to Problem 1QQ

The correct option is B.

Explanation of Solution

Given Information: The equation of the function is $y={\sin }^4\left(3x\right)$

Calculation:

The derivative of the function with respect to x is,

  $\begin{array}{c}\frac{dy}{dx}=\frac{d}{dx}\left({\sin }^4\left(3x\right)\right)\left(\text{Substitute }y={\sin }^4\left(3x\right)\right)\\ =4{\sin }^3\left(3x\right)\times \frac{d}{dx}\left(\sin \left(3x\right)\right)\left(\text{Apply chain rule}\right)\\ =4{\sin }^3\left(3x\right)\times \cos \left(3x\right)\times \frac{d}{dx}\left(3x\right)\\ =12{\sin }^3\left(3x\right)\cos \left(3x\right)\end{array}$