Answer
$p' = sec^{2}q$
Work Step by Step
$\displaystyle p = \frac{sinq + cosq}{cosq}$
$\displaystyle p' = \frac{cosq(cosq -sinq) + (sinq+cosq)sinq}{cos^{2}q}$
$\displaystyle p' = \frac{cos^{2}q - sinq\ cosq + sin^{2}q + sinq\ cosq}{cos^{2}q}$
$\displaystyle p' = \frac{1}{cos^{2}q}$
$\displaystyle p' = sec^{2}q$
