91Ó°ÊÓ

Write derivative formulas for the functions. $$ f(x)=(19+12 \ln 2 x)(17-3 \ln 4 x) $$

For Activities 11 through 28 a. write the product function. b. write the rate-of-change function. $$ g(x)=5 e^{2 x} ; b(x)=20 x^{3}-30 $$

Evaluate the limit. If the limit is of an indeterminate form, indicate the form and use L'Hôpital's Rule to evaluate the limit. $$ \lim _{x \rightarrow 4} \frac{x-4}{(x+4)^{0.3}-2} $$

Write derivative formulas for the functions. $$ f(x)=4 x \sqrt{3 x+2}+93 $$

Give the derivative formula for each function. \(\quad n(x)=14 \sin x\)

In Activities 9 through \(16,\) for each pair of functions, write the composite function and its derivative in terms of one input variable. $$ p(t)=7.9 \sin t ; t(k)=14 k^{3}-12 k^{2} $$

Evaluate the limit. If the limit is of an indeterminate form, indicate the form and use L'Hôpital's Rule to evaluate the limit. $$ \lim _{x \rightarrow 2} \frac{2 x^{2}-5 x+2}{5 x^{2}-7 x-6} $$

In Activities 1 through \(26,\) write the formula for the derivative of the function. $$ f(x)=12 x^{4}+13 x^{3}+5 $$

In Activities 1 through \(30,\) for each of the composite functions, identify an inside function and an outside function and write the derivative with respect to \(x\) of the composite function. $$ f(x)=\sqrt{x^{2}-3 x} $$

In Activities 1 through \(30,\) for each of the composite functions, identify an inside function and an outside function and write the derivative with respect to \(x\) of the composite function. $$ f(x)=\sqrt[3]{x^{2}+5 x} $$