Chapter 4.1, Problem 25E

To determine

To calculate:The differentiation of the given function.

Answer to Problem 25E

The differentiation is $-{\sec }^2(2-\theta )$ .

Explanation of Solution

Given information: Given function is $r=\tan (2-\theta )$ .

Formula used: $\frac{d(\tan x)}{dx}={\sec }^{2}x$ with chain and subtraction rule.

Calculation:

  $r=\tan (2-\theta )$

Differentiate with respect to $\theta$ ,

  $\begin{array}{l}\frac{dr}{d\theta }=\frac{d[\tan (2-\theta )]}{d(2-\theta )}\times \frac{d(2-\theta )}{d\theta }\\ \frac{dr}{d\theta }={\sec }^2(2-\theta )\times (-1)\\ \frac{dr}{d\theta }=-{\sec }^2(2-\theta )\end{array}$