91Ó°ÊÓ

Find the derivative of each function. $$ f(x)=x^{4} $$

Find functions \(f\) and \(g\) such that the given function is the composition \(f(g(x))\). $$ \sqrt{x^{2}-3 x+1} $$

Find the derivative of each function in two ways: a. Using the Product Rule. b. Multiplying out the function and using the Power Rule. Your answers to parts (a) and (b) should agree. $$ x^{4} \cdot x^{6} $$

1-4. Complete the tables and use them to find the given limits. Round calculations to three decimal places. A graphing calculator with a TABLE feature will be very helpful. a. \(\lim _{x \rightarrow 2^{-}}(5 x-7)\) b. \(\lim _{x \rightarrow 2^{+}}(5 x-7)\) c. \(\lim _{x \rightarrow 2}(5 x-7)\)

Find the derivative of each function. $$ f(x)=x^{5} $$

Complete the tables and use them to find the given limits. Round calculations to three decimal places. A graphing calculator with a TABLE feature will be very helpful. a. \(\lim _{x \rightarrow 4^{-}}(2 x+1)\) b. \(\lim _{x \rightarrow 4^{+}}(2 x+1)\) c. \(\lim _{x \rightarrow 4}(2 x+1)\)

Find functions \(f\) and \(g\) such that the given function is the composition \(f(g(x))\). $$ \left(5 x^{2}-x+2\right)^{4} $$

Find the derivative of each function in two ways: a. Using the Product Rule. b. Multiplying out the function and using the Power Rule. Your answers to parts (a) and (b) should agree. $$ x^{7} \cdot x^{2} $$

Find the derivative of each function in two ways: a. Using the Product Rule. b. Multiplying out the function and using the Power Rule. Your answers to parts (a) and (b) should agree. $$ x^{4}\left(x^{5}+1\right) $$

Find functions \(f\) and \(g\) such that the given function is the composition \(f(g(x))\). $$ \left(x^{2}-x\right)^{-3} $$