Chapter 4, Problem 9RE

To determine

The derivative of the given function.

Answer to Problem 9RE

The derivative is $3\sec (1+3\theta )\tan (1+3\theta )$ .

Explanation of Solution

Given information: Given function $r=\sec (1+3\theta )$

Formula used: $\frac{d(x)}{dx}=1\text{and}\frac{d(\sec x)}{dx}=\sec x\tan x$ with chain rule.

Calculation:

  $\begin{array}{l}r=\sec (1+3\theta )\\ \text{Differentiate}\text{with}\text{respect}\text{to}\theta \\ \frac{dr}{d\theta }=\frac{d\sec (1+3\theta )}{d(1+3\theta )}\times \frac{d(1+3\theta )}{d\theta }\\ \frac{dr}{d\theta }=\sec (1+3\theta )\tan (1+3\theta )\times 3\\ \frac{dr}{d\theta }=3\sec (1+3\theta )\tan (1+3\theta )\end{array}$