91Ó°ÊÓ

Finding the Slope of a Graph In Exercises \(31-38,\) find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. $$\begin{array}{ll}{\text { Function }} & {\text { Point }} \\ {\text { 31. } f(x)=\frac{8}{x^{2}}} & {\text { (2, } 2}\end{array}$$

Finding a Derivative IIn Exercises \(9-34,\) find the derivative of the function. \(s(t)=\left(\frac{1+t}{t+3}\right)^{4}\)

\(\begin{array}{l}{\text { Finding an Equation of a Tangent Line In }} \\\ {\text { Exercises } 29-36 \text { , (a) find an equation of the tangent }} \\\ {\text { line to the graph of } f \text { at the given point, (b) use }} \\\ {\text { a graphing utility to graph the function and its }} \\ {\text {tangent line at the point, and (c) use the tangent }} \\ {\text { feature of a graphing utility to confirm your results. }}\end{array}\) $$f(x)=x^{3}, \quad(2,8)$$

Finding the Slope of a Graph In Exercises \(25-32,\) find \(d y / d x\) by implicit differentiation. Then find the slope of the graph at the given point. \(x \cos y=1, \quad\left(2, \frac{\pi}{3}\right)\)

Finding a Derivative In Exercises \(29-40\) , find the derivative of the alvebraic function. \(f(x)=x^{4}\left(1-\frac{2}{x+1}\right)\)

Finding a Derivative IIn Exercises \(9-34,\) find the derivative of the function. \(g(x)=\left(\frac{3 x^{2}-2}{2 x+3}\right)^{-2}\)

\(\begin{array}{l}{\text { Finding an Equation of a Tangent Line In }} \\\ {\text { Exercises } 29-36 \text { , (a) find an equation of the tangent }} \\\ {\text { line to the graph of } f \text { at the given point, (b) use }} \\\ {\text { a graphing utility to graph the function and its }} \\ {\text {tangent line at the point, and (c) use the tangent }} \\ {\text { feature of a graphing utility to confirm your results. }}\end{array}\) $$f(x)=x^{3}+1, \quad(-1,0)$$

Finding the Slope of a Graph In Exercises \(31-38\) , find the slope of the graph of the function at the given point. Use the derivative feature of a graphing utility to confirm your results. $$f(t)=2-\frac{4}{t}$$ (4,1)

Finding a Derivative IIn Exercises \(9-34,\) find the derivative of the function. \(f(x)=\left(\left(x^{2}+3\right)^{5}+x\right)^{2}\)

Finding a Derivative In Exercises \(29-40\) , find the derivative of the alvebraic function. \(f(x)=\frac{3 x-1}{\sqrt{x}}\)