Chapter 7: Problem 9
Find the derivative of the function. $$ f(x)=4 x+1 $$
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Find the derivative of the function. State which differentiation rule(s) you used to find the derivative. $$ y=\left(\frac{6-5 x}{x^{2}-1}\right)^{2} $$
The cost of producing \(x\) units of a product is given by \(C=x^{3}-15 x^{2}+87 x-73, \quad 4 \leq x \leq 9\) (a) Use a graphing utility to graph the marginal cost function and the average cost function, \(C / x\), in the same viewing window. (b) Find the point of intersection of the graphs of \(d C / d x\) and \(C / x\). Does this point have any significance?
Use the General Power Rule to find the derivative of the function. $$ y=\sqrt[3]{3 x^{3}+4 x} $$
Identify the inside function, \(u=g(x)\), and the outside function, \(y=f(u)\). $$ y=f(g(x)) \quad u=g(x) \quad y=f(u) $$ $$ y=(x+2)^{-1 / 2} $$
Match the function with the rule that you would use to find the derivative most efficiently. (a) Simple Power Rule (b) Constant Rule (c) General Power Rule (d) Quotient Rule $$ f(x)=\frac{2}{x-2} $$
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