Chapter 9

In Exercises 1-48, find the derivative of each function. \(f(x)=(2 x-1)^{4}\)

In Exercises 1-30, find the derivative of each function. \(f(x)=2 x\left(x^{2}+1\right)\)

In Exercises 1-34, find the derivative of the function \(f\) by using the rules of differentiation. \(f(x)=-3\)

Find the derivative of each function. \(f(x)=(1-x)^{3}\)

Find the derivative of each function. \(f(x)=3 x^{2}(x-1)\)

Find the derivative of the function \(f\) by using the rules of differentiation. \(f(x)=365\)

Find the derivative of each function. \(f(x)=\left(x^{2}+2\right)^{5}\)

Find the derivative of each function. \(f(t)=(t-1)(2 t+1)\)

Find the derivative of the function \(f\) by using the rules of differentiation. \(f(x)=x^{5}\)

Find the derivative of each function. \(f(t)=2\left(t^{3}-1\right)^{5}\)

Find the derivative of each function. \(f(x)=(2 x+3)(3 x-4)\)

Find the derivative of the function \(f\) by using the rules of differentiation. \(f(x)=x^{7}\)

Find the derivative of each function. \(f(x)=\left(2 x-x^{2}\right)^{3}\)

Find the derivative of each function. \(f(x)=(3 x+1)\left(x^{2}-2\right)\)

Find the derivative of the function \(f\) by using the rules of differentiation. \(f(x)=x^{2.1}\)

Find the derivative of each function. \(f(x)=3\left(x^{3}-x\right)^{4}\)

Find the derivative of each function. \(f(x)=(x+1)\left(2 x^{2}-3 x+1\right)\)

Find the derivative of the function \(f\) by using the rules of differentiation. \(f(x)=x^{0.8}\)

Find the derivative of each function. \(f(x)=(2 x+1)^{-2}\)

Find the derivative of each function. \(f(x)=\left(x^{3}-1\right)(x+1)\)

Find the derivative of the function \(f\) by using the rules of differentiation. \(f(x)=3 x^{2}\)

Find the derivative of each function. \(f(t)=\frac{1}{2}\left(2 t^{2}+t\right)^{-3}\)

Find the derivative of each function. \(f(x)=\left(x^{3}-12 x\right)\left(3 x^{2}+2 x\right)\)

Find the derivative of the function \(f\) by using the rules of differentiation. \(f(x)=-2 x^{3}\)

Find the derivative of each function. \(f(x)=\left(x^{2}-4\right)^{3 / 2}\)

Find the derivative of each function. \(f(w)=\left(w^{3}-w^{2}+w-1\right)\left(w^{2}+2\right)\)

Find the derivative of the function \(f\) by using the rules of differentiation. \(f(r)=\pi r^{2}\)

In Exercises 9-16, use the four-step process to find the slope of the tangent line to the graph of the given function at any point. \(f(x)=13\)

In Exercises 9-16, complete the table by computing \(f(x)\) at the given values of \(x\). Use these results to estimate the indicated limit (if it exists). $$ \begin{array}{l} f(x)=x^{2}+1 ; \lim _{x \rightarrow 2} f(x) \\ \hline x \quad 1.9 \quad 1.99 \quad 1.999 \quad 2.001 \quad 2.01 \quad 2.1 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & & & & & & \\ \hline \end{array} $$

Find the derivative of each function. \(f(t)=\left(3 t^{2}-2 t+1\right)^{3 / 2}\)

Find the derivative of each function. \(f(x)=\frac{1}{5} x^{5}+\left(x^{2}+1\right)\left(x^{2}-x-1\right)+28\)

Find the derivative of the function \(f\) by using the rules of differentiation. \(f(r)=\frac{4}{3} \pi r^{3}\)

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. \(f(x)=-6\)

Complete the table by computing \(f(x)\) at the given values of \(x\). Use these results to estimate the indicated limit (if it exists). $$ \begin{array}{l} f(x)=2 x^{2}-1 ; \lim _{x \rightarrow 1} f(x) \\ \hline x \quad 0.9 \quad 0.99 \quad 0.999 \quad 1.001 \quad 1.01 \quad 1.1 \\ \hline f(\boldsymbol{x}) & & & & & & \\ \hline \end{array} $$

Find the derivative of each function. \(f(x)=\sqrt{3 x-2}\)

Find the derivative of each function. \(f(x)=\left(5 x^{2}+1\right)(2 \sqrt{x}-1)\)

Find the derivative of the function \(f\) by using the rules of differentiation. \(f(x)=9 x^{1 / 3}\)

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. \(f(x)=2 x+7\)

Complete the table by computing \(f(x)\) at the given values of \(x\). Use these results to estimate the indicated limit (if it exists). $$ \begin{array}{l} f(x)=\frac{|x|}{x} ; \lim _{x \rightarrow 0} f(x)\\\ \begin{array}{lllllll} \hline \boldsymbol{x} & -0.1 & -0.01 & -0.001 & 0.001 & 0.01 & 0.1 \\ \hline \boldsymbol{f}(\boldsymbol{x}) & & & & & & \\ \hline \end{array} \end{array} $$

Find the derivative of each function. \(f(t)=\sqrt{3 t^{2}-t}\)

Find the derivative of each function. \(f(t)=(1+\sqrt{t})\left(2 t^{2}-3\right)\)

Find the derivative of the function \(f\) by using the rules of differentiation. \(f(x)=\frac{5}{4} x^{4 / 5}\)

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. \(f(x)=8-4 x\)

Complete the table by computing \(f(x)\) at the given values of \(x\). Use these results to estimate the indicated limit (if it exists). $$ \begin{array}{l} f(x)=\frac{|x-1|}{x-1} ; \lim _{x \rightarrow 1} f(x) \\ \hline x \quad 0.9 \quad 0.99 \quad 0.999 \quad 1.001 \quad 1.01 \quad 1.1 \\ \hline f(x) \end{array} $$

Find the derivative of each function. \(f(x)=\sqrt[3]{1-x^{2}}\)

Find the derivative of each function. \(f(x)=\left(x^{2}-5 x+2\right)\left(x-\frac{2}{x}\right)\)

Find the derivative of the function \(f\) by using the rules of differentiation. \(f(x)=3 \sqrt{x}\)

Use the four-step process to find the slope of the tangent line to the graph of the given function at any point. \(f(x)=3 x^{2}\)

Complete the table by computing \(f(x)\) at the given values of \(x\). Use these results to estimate the indicated limit (if it exists). $$ \begin{array}{l} f(x)=\frac{1}{(x-1)^{2}} ; \lim _{x \rightarrow 1} f(x) \\ \hline \boldsymbol{x} \quad 0.9 \quad 0.99 \quad 0.999 \quad 1.001 \quad 1.01 \quad 1.1 \\ \hline \boldsymbol{f}(\boldsymbol{x}) \end{array} $$

Find the derivative of each function. \(f(x)=\sqrt{2 x^{2}-2 x+3}\)