91Ó°ÊÓ

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

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

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

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

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

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

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