Question

find \\( \frac{d p}{d q} \\) for \\( p=\frac{\cos q+\sin q}{\cos q} \\).
\\( \frac{d p}{d q}=\square \\)

Explanation:

Step1: Simplify the function

First, simplify \( p=\frac{\cos q+\sin q}{\cos q}=1 + \tan q\) (since \(\frac{\sin q}{\cos q}=\tan q\)).

Step2: Differentiate using basic rules

Differentiate \(p = 1+\tan q\) with respect to \(q\).
The derivative of a constant \(1\) is \(0\), and the derivative of \(\tan q\) with respect to \(q\) is \(\sec^{2}q\) (using the formula \(\frac{d}{dq}(\tan q)=\sec^{2}q\)).

Answer:

\(\sec^{2}q\)