Final answer:
The derivative of the function f(x) = 2 sec(x) − 3x is found by differentiating each term individually. The derivative of 2 sec(x) is 2 sec(x) tan(x), and the derivative of − 3x is −3. Hence, the combined result is f '(x) = 2 sec(x) tan(x) − 3.
Step-by-step explanation:
You asked to find the derivative of the function f(x) = 2 sec(x) − 3x. To do this, we will differentiate each term of the function individually, using the rules of differentiation.
Firstly, the derivative of 2 sec(x) is 2 sec(x) tan(x), because the derivative of sec(x) is sec(x) tan(x), and we multiply that by the constant coefficient 2.
Secondly, the derivative of − 3x is simply −3, as the derivative of x with respect to x is 1, and then we multiply that by −3.
Combining these results, the derivative of the function, denoted as f '(x), is f '(x) = 2 sec(x) tan(x) − 3.
This method of finding a derivative is known as differentiation, and it's a fundamental tool in calculus used to determine the instantaneous rate of change of a function.