91Ó°ÊÓ

Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ h(t)=\frac{t+2}{t^{2}+5 t+6} $$

Sketch the graph of the function and describe the interval(s) on which the function is continuous. \(f(x)=\frac{5}{x^{2}+1} \quad[-2,2]\)

Sketch the graph of the function and describe the interval(s) on which the function is continuous. \(f(x)=\frac{1}{x-2}\) \([1,4]\)

find \(f^{\prime}(x)\). $$ f(x)=x^{2}-2 x-\frac{2}{x^{4}} $$

Use the General Power Rule to find the derivative of the function. $$ f(x)=-3 \sqrt[4]{2-9 x} $$

The monthly demand function and cost function for \(x\) newspapers at a newsstand are given by \(p=5-0.001 x\) and \(C=35+1.5 x\) (a) Find the monthly revenue \(R\) as a function of \(x\). (b) Find the monthly profit \(P\) as a function of \(x\). (c) Complete the table. $$ \begin{array}{|l|l|l|l|l|l|} \hline x & 600 & 1200 & 1800 & 2400 & 3000 \\ \hline d R / d x & & & & & \\ \hline d P / d x & & & & & \\ \hline P & & & & & \\ \hline \end{array} $$

Use the limit definition to find the derivative of the function. $$ f(x)=\frac{1}{x+2} $$

Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ g(s)=\frac{s^{2}-2 s+5}{\sqrt{s}} $$

Find the limit. $$ \lim _{x \rightarrow 3} \frac{\sqrt{x+1}-1}{x} $$

Use the limit definition to find the derivative of the function. $$ g(s)=\frac{1}{s-1} $$