91Ó°ÊÓ

In Activities 9 through \(16,\) for each pair of functions, write the composite function and its derivative in terms of one input variable. $$ b(p)=\frac{4}{p} ; p(t)=1+3 e^{-0.5 t} $$

In Activities 1 through \(26,\) write the formula for the derivative of the function. $$ f(x)=23 x^{7} $$

Evaluate the limit. If the limit is of an indeterminate form, indicate the form and use L'Hôpital's Rule to evaluate the limit. $$ \lim _{x \rightarrow 2} \frac{3 x-6}{x+2} $$

Give the derivative formula for each function. \(\quad j(x)=4 \ln x-e^{\pi}\)

Evaluate the limit. If the limit is of an indeterminate form, indicate the form and use L'Hôpital's Rule to evaluate the limit. $$ \lim _{x \rightarrow 7} \frac{x^{2}-2 x-35}{7 x-x^{2}} $$

Give the derivative formula for each function. \(\quad j(x)=-\ln x+\frac{1}{2 e^{4}}\)

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. $$ f(x)=\left(5 x^{2}+3 x+7\right)^{-1} $$

In Activities 1 through \(26,\) write the formula for the derivative of the function. $$ p(t)=\frac{2}{7} t^{3} $$

Write derivative formulas for the functions. $$ f(x)=\left[\ln \left(15.7 x^{3}\right)\right]\left(e^{15.7 x^{3}}\right) $$

For Activities 11 through 28 a. write the product function. b. write the rate-of-change function.] $$ g(x)=3 x^{-0.7} ; h(x)=5^{x} $$