91Ó°ÊÓ

Finding a Derivative In Exercises \(33-54,\) find the derivative. $$ y=e^{x-4} $$

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 \(f^{-1} .\) \(f(x)=x^{5}\)

Verify each identity. (a) arccsc \(x=\arcsin \frac{1}{x}, \quad x \geq 1\) (b) \(\arctan x+\arctan \frac{1}{x}=\frac{\pi}{2}, \quad x>0\)

Finding an Indefinite Integral of a Trigonometric Function In Exercises \(31-40\) , find the indefinite integral. $$ \int \frac{x}{x^{2}-3} d x $$

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 \(f^{-1} .\) \(f(x)=x^{3}-1\)

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 \(33-54,\) find the derivative. $$ y=5 e^{x^{2}+5} $$

In Exercises 37–40, find the limit. $$ \lim _{x \rightarrow 6^{-}} \ln (6-x) $$

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.) $$ f(x)=3^{4 x} $$

In Exercises 37–40, find any relative extrema of the function. Use a graphing utility to confirm your result. $$ f(x)=x \sinh (x-1)-\cosh (x-1) $$