91Ó°ÊÓ

Find the derivative of \(y\) with respect to the appropriate variable. $$y=\cos ^{-1}\left(e^{-t}\right)$$

Find the derivatives of the functions. $$y=(1+2 x) e^{-2 x}$$

Find the derivatives of the functions in Exercises \(17-40 .\) $$w=\frac{1}{z^{1.4}}+\frac{\pi}{\sqrt{z}}$$

Graph the curves over the given intervals, together with their tangent lines at the given values of \(x .\) Label each curve and tangent line with its equation. $$\begin{aligned}&y=\tan x, \quad-\pi / 2

Find the derivative of \(y\) with respect to \(x, t,\) or \(\theta\) as appropriate. $$y=\ln (\sec (\ln \theta))$$

Find the derivatives of the functions. $$y=\left(x^{2}-2 x+2\right) e^{5 x / 2}$$

Graph the curves over the given intervals, together with their tangent lines at the given values of \(x .\) Label each curve and tangent line with its equation. $$\begin{aligned}&y=\sec x, \quad-\pi / 2

Motion in the plane The coordinates of a particle in the metric \(x y\) -plane are differentiable functions of time \(t\) with \(-d x / d t=-1 \mathrm{m} / \sec\) and \(d y / d t=-5 \mathrm{m} / \mathrm{sec} .\) How fast is the par- ticle's distance from the origin changing as it passes through the point (5,12)\(?\)

Find the derivatives of the functions in Exercises \(17-40 .\) $$y=\sqrt[7]{x^{2}}-x^{2}$$

Find the derivative of \(y\) with respect to the appropriate variable. $$y=s \sqrt{1-s^{2}}+\cos ^{-1} s$$