Final answer:
To evaluate P = 3q + tan(q)/q sec(q) and find dP/dq, simplify the expression and differentiate P with respect to q using the quotient rule.
Step-by-step explanation:
To evaluate P = 3q + tan(q)/q sec(q) and find dP/dq, we can start by simplifying the expression. Let's use the trigonometric identity tan(q) = sin(q)/cos(q).
So, P = 3q + sin(q)/(q cos(q)).
To find dP/dq, we differentiate P with respect to q. Using the quotient rule, dP/dq = (3 - (q cos(q) - sin(q))/(q^2 cos(q))).