Chapter 14.4, Problem 73E

To determine

a)

Use the relation $f\text{'}(x)=\tan \theta$ prove that $\frac{d\theta }{dx}=\frac{f\text{'}\text{'}(x)}{(1+f\text{'}{(x)}^2)}$

To determine

b)

Use the are length integral to show that $\frac{ds}{dx}=\sqrt{1+f\text{'}{(x)}^2}$

To determine

c)

Now given a proof of using equation