91Ó°ÊÓ

Finding an Inverse Function In Exercises \(35-46\) , (a) find the inverse function of \(f,\) (b) graph \(f\) and \(f^{-1}\) on the same set of coordinate axes, (c) describe the relationship between the graphs, and (d) state the domains and ranges of \(f\) and \(f^{-1}\) . $$f(x)=\frac{x+2}{x}$$

Finding a Derivative In Exercises \(43-66,\) find the derivative of the function. $$h(x)=\ln \left(2 x^{2}+1\right)$$

In Exercises \(41-56,\) find the derivative of the function. $$f(x)=\operatorname{arccot} \sqrt{x}$$

In Exercises \(33-54,\) find the derivative of the function. $$y=\ln \left(\frac{1+e^{x}}{1-e^{x}}\right)$$

In Exercises \(41-56,\) find the derivative of the function. $$g(x)=\frac{\arcsin 3 x}{x}$$

In Exercises 47-50, find the indefinite integrals, if possible, using the formulas and techniques you have studied so far in the text. $$\begin{array}{l}{\text { (a) } \int \frac{1}{\sqrt{1-x^{2}}} d x} \\ {\text { (b) } \int \frac{x}{\sqrt{1-x^{2}}} d x} \\ {\text { (c) } \int \frac{1}{x \sqrt{1-x^{2}}} d x}\end{array}$$

Finding a Derivative In Exercises \(43-66,\) find the derivative of the function. $$y=(\ln x)^{4}$$

In Exercises \(33-54,\) find the derivative of the function. $$y=\frac{2}{e^{x}+e^{-x}}$$

In Exercises 47 and \(48,\) find the particular solution of the differential equation that satisfies the initial conditions. $$f^{\prime \prime}(x)=\frac{2}{x^{2}}, \quad f^{\prime}(1)=1, \quad f(1)=1, \quad x>0$$

Finding a Derivative In Exercises \(39-60,\) find the derivative of the function. $$h(\theta)=2^{-\theta} \cos \pi \theta$$