Question

Let f(x) = sec(x) - x. Find f '(x).

Answer 1

The derivative of the function f(x) = sec(x) - x is found by differentiating each term separately. The derivative of sec(x) is sec(x)tan(x), and the derivative of -x is -1. Therefore, the derivative of f(x), f '(x), is sec(x)tan(x) - 1.

Step-by-step explanation:

To find the derivative of the function f(x) = sec(x) - x, we need to apply the rules for differentiation. The derivative of sec(x) concerning x is sec(x)tan(x), and the derivative of -x concerning x is -1. Therefore, the derivative of f(x), denoted as f '(x), is the sum of the derivatives of each term.

So, f '(x) = sec(x)tan(x) - 1.

A step-by-step explanation would look like this:

1. Identify the individual functions within f(x) that require differentiation: sec(x) and -x.
2. Use the derivative rule for sec(x), which is sec(x)tan(x).
3. Recognize that the derivative of -x is -1.
4. Combine the derivatives of the individual terms to find the overall derivative of f(x).
5. Conclude that f '(x) = sec(x)tan(x) - 1.