91Ó°ÊÓ

Finding a Derivative In Exercises \(43-66,\) find the derivative of the function. $$f(x)=\ln 3 x$$

In Exercises \(41-56,\) find the derivative of the function. $$g(x)=3 \arccos \frac{x}{2}$$

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 \(f^{-1}\) . $$f(x)=x^{2 / 3}, \quad x \geq 0$$

In Exercises 43-46, use the specified substitution to find or evaluate the integral. $$\begin{array}{l}{\int \frac{\sqrt{x-2}}{x+1} d x} \\\ {u=\sqrt{x-2}}\end{array}$$

In Exercises \(33-54,\) find the derivative of the function. $$g(t)=e^{-3 / t^{2}}$$

Finding a Derivative In Exercises \(39-60,\) find the derivative of the function. $$y=-7 x\left(8^{-2 x}\right)$$

Finding a Derivative In Exercises \(43-66,\) find the derivative of the function. $$f(x)=\ln (x-1)$$

In Exercises \(41-56,\) find the derivative of the function. $$f(x)=\operatorname{arcsec} 2 x$$

In Exercises \(33-54,\) find the derivative of the function. $$y=\ln \left(2-e^{5 x}\right)$$

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 \(f^{-1}\) . $$f(x)=\frac{x}{\sqrt{x^{2}+7}}$$