Question

a graphing calculator is recommended. let f(x) = sec(x) - x. (a) find f(x). f(x) = (b) check to see that your answer to part (a) is reasonable by graphing f and f for |x| < π/2.

Explanation:

Step1: Recall derivative rules

The derivative of $\sec(x)$ is $\sec(x)\tan(x)$ and the derivative of $x$ is $1$.

Step2: Apply sum - difference rule

If $f(x)=u(x)-v(x)$, then $f^{\prime}(x)=u^{\prime}(x)-v^{\prime}(x)$. Here $u(x)=\sec(x)$ and $v(x) = x$. So $f^{\prime}(x)=\sec(x)\tan(x)-1$.

Answer:

$\sec(x)\tan(x)-1$