91Ó°ÊÓ

Differentiate two ways: first, by using the Quotient Rule; then, by dividing the expressions before differentiating. Compare your results as a check. Use a graphing calculator to check your results. \(y=\frac{t^{2}-16}{t+4}\)

Find \(f^{\prime \prime}(x)\) $$ f(x)=\left(x^{3}+2 x\right)^{6} $$

The initial substitution of \(x=a\) yields the form \(0 / 0 .\) Look for ways to simplify the function algebraically, or use a table or graph to determine the limit. When necessary, state that the limit does not exist. $$ \lim _{x \rightarrow 5} \frac{x^{2}-25}{x-5} $$

Differentiate each function $$ f(x)=x^{2}+(100-x)^{2} $$

Find \(\frac{d y}{d x}\). $$ y=\frac{1}{2} x^{4 / 5} $$

Differentiate two ways: first, by using the Quotient Rule; then, by dividing the expressions before differentiating. Compare your results as a check. Use a graphing calculator to check your results. \(y=\frac{t^{2}-25}{t-5}\)

Find an equation of the tangent line to the graph of \(f(x)=-1 / x\) at (a) (-1,1)\(;\) (b) \(\left(2,-\frac{1}{2}\right) ;\) (c) \(\left(-5, \frac{1}{5}\right)\).

Differentiate each function. \(g(x)=\left(5 x^{2}+4 x-3\right)\left(2 x^{2}-3 x+1\right)\)

Differentiate each function $$ G(x)=\sqrt[3]{2 x-1}+(4-x)^{2} $$

The initial substitution of \(x=a\) yields the form \(0 / 0 .\) Look for ways to simplify the function algebraically, or use a table or graph to determine the limit. When necessary, state that the limit does not exist. $$ \lim _{x \rightarrow-2} \frac{x^{2}-2 x-8}{x^{2}-4} $$