Chapter 3, Problem 30RE

To determine

To calculate: The derivative of the function.

Answer to Problem 30RE

The derivative of the function is 0.

Explanation of Solution

Given Information: The function is $y=\frac{\sin x\cot x}{\cos x}$ .

Calculation:

The given function is,

  $y=\frac{\sin x\cot x}{\cos x}$

Simplify the function as follows:

  $\begin{array}{c}y=\frac{\sin x\cot x}{\cos x}\\ =\frac{\sin x\times \frac{\cos x}{\sin x}}{\cos x}\left(\because \cot x=\frac{\cos x}{\sin x}\right)\\ =\frac{\cos x}{\cos x}\\ =1\end{array}$

The derivative of the function y with respect to x is calculated as,

  $\begin{array}{c}y=1\\ \frac{dy}{dx}=\frac{d}{dx}\left(1\right)\\ =0\left(\text{Since derivative of a constant is 0}\right)\end{array}$

Conclusion:

The derivative of the function is 0.