Final answer:
The derivative of the function f(x) = 4 sec(x) − 5x is f '(x) = 4 sec(x) tan(x) - 5.
Step-by-step explanation:
The student's question is asking to find the derivative of the function f(x) = 4 sec(x) − 5x. To find f '(x), the derivative of each term in the function must be calculated separately using basic differentiation rules.
The derivative of 4 sec(x) with respect to x is 4 sec(x) tan(x), since the derivative of sec(x) is sec(x) tan(x). The derivative of − 5x is simply − 5, as the derivative of any constant times x is the constant itself.
So, combining these derivatives, the derivative of f(x) is:
f '(x) = 4 sec(x) tan(x) - 5