91Ó°ÊÓ

Finding a Derivative In Exercises \(37-58\) , find the derivative of the function. (Hint: In some exercises, you may find it helpful to apply logarithmic properties before differentiating.) $$ f(x)=3^{4 x} $$

Completing the Square In Exercises \(33-42,\) find or evaluate the integral by completing the square. $$ \int \frac{2}{\sqrt{-x^{2}+4 x}} d x $$

Finding a Derivative In Exercises \(37-58\) , find the derivative of the function. (Hint: In some exercises, you may find it helpful to apply logarithmic properties before differentiating.) $$ y=5^{-4 x} $$

Completing the Square In Exercises \(33-42,\) find or evaluate the integral by completing the square. $$ \int_{2}^{3} \frac{2 x-3}{\sqrt{4 x-x^{2}}} d x $$

Finding a Derivative In Exercises \(33-54,\) find the derivative. $$ y=e^{x} \ln x $$

Find the inverse function of \(f,(\mathbf{b})\) graph \(f\) and \(f^{-1}\) on the same set of coordinate axes, ( \(\mathbf{c} )\) describe the relationship between the graphs, and ( \(\mathbf{d} )\) state the domain and range of \(f\) and \(f^{-1} .\) \(f(x)=\sqrt{x}\)

Finding an Indefinite Integral of a Trigonometric Function In Exercises \(31-40\) , find the indefinite integral. $$ \int \frac{\sec x \tan x}{\sec x-1} d x $$

In Exercises 37–40, find the limit. $$ \lim _{x \rightarrow 2^{-}} \ln \left[x^{2}(3-x)\right] $$

In Exercises 37–40, find any relative extrema of the function. Use a graphing utility to confirm your result. $$ g(x)=x \operatorname{sech} x $$

Find the derivative of the function. \(f(x)=2 \arcsin (x-1)\)