Determine the slope of the tangent line to the curve defined by $y={\tan }^{-1}x$ at the point where $x=1$.

Evaluate the following derivative using the table given below.

${\left(h^{-1}\right)}^{\prime }\left(9\right)$

Without finding the derivative of $y={\cos }^{-1}x$, determine the slope of the line tangent to $y={\cos }^{-1}x$ at $(\frac{1}{2},\frac{\pi }{3})$.

Graph the derivative of $g\left(x\right)=\left(x-1\right)\cos^{-1}\left(x\right)$ on $\left\lbrack-1,1\right\rbrack$.

A woman stands on a flat ground surface at the base of a $90\text{ ft}$ tall observation tower. A hawk takes off from the top of the tower, descending at an angle of $45^{\circ}$ below the horizontal.

Determine the rate at which the angle of elevation $\theta$ is changing with respect to the height of the hawk when it is located $65\text{ ft}$ above the ground.