91Ó°ÊÓ

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. $$ f(x)=\frac{8}{(x-1)^{3}} $$

Evaluate the limit. If the limit is of an indeterminate form, indicate the form and use L'Hôpital's Rule to evaluate the limit. $$ \lim _{x \rightarrow 5} \frac{(x-1)^{0.5}-2}{x^{2}-25} $$

In Activities 9 through \(16,\) for each pair of functions, write the composite function and its derivative in terms of one input variable. $$ k(t)=4.3 t^{3}-2 t^{2}+4 t-12 ; t(x)=\ln x $$

In Activities 1 through \(26,\) write the formula for the derivative of the function. $$ f(x)=-0.5 x^{2} $$

Give the derivative formula for each function. \(\quad g(x)=12-7 \ln x\)

Write derivative formulas for the functions. $$ f(x)=\frac{430\left(0.62^{x}\right)}{6.42+3.3\left(1.46^{x}\right)} $$

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. $$ \lim _{x \rightarrow 4} \frac{x-4}{(x+4)^{0.3}-2} $$

In Activities 9 through \(16,\) for each pair of functions, write the composite function and its derivative in terms of one input variable. $$ f(x)=\ln x ; x(t)=5 t+11 $$

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