Chapter 4, Problem 5RE

To determine

To Find: The derivative of the given function.

Answer to Problem 5RE

The derivative is $2\sin (1-2t)$ .

Explanation of Solution

Given information: Given function $s=\cos (1-2t)$

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

Calculation:

  $\begin{array}{l}s=\cos (1-2t)\\ \text{Differentiate}\text{with}\text{respect}\text{to}t\\ \frac{ds}{dt}=\frac{d\cos (1-2t)}{d(1-2t)}\times \frac{d(1-2t)}{dt}\\ \frac{ds}{dt}=-\sin (1-2t)\times -2\\ \frac{ds}{dt}=2\sin (1-2t)\end{array}$