Exercise · ZW-QUOTIENT-RULE-010 · ★★☆ Intermediate
Compute \(f'(1)\) if \(f(x)=\frac{2x+1}{x^{2}}\).
Choose one option.
Show answer
- B. \(-4\)
Explanation
With \(u=2x+1\) and \(v=x^{2}\): \(f'(x)=\frac{2x^{2}-(2x+1)2x}{x^{4}}=\frac{-2(x+1)}{x^{3}}\), and at \(x=1\) it gives \(-4\).
Review the concept: Quotient rule
The derivative of a quotient \(\frac{f}{g}\), with \(g\ne0\), is \(\frac{f^{\prime}g-fg^{\prime}}{g^2}\).
\[\left(\frac{f}{g}\right)'=\frac{f'g-f\,g'}{g^{2}}\]
More practice problems: quotient rule
- ZW-QUOTIENT-RULE-001 In the quotient rule ((f)/(g))', what is the correct numerator?
- ZW-QUOTIENT-RULE-002 Differentiate f(x)=(x)/(x + 1).
- ZW-QUOTIENT-RULE-003 Differentiate f(x)=(sin x)/(x).
- ZW-QUOTIENT-RULE-004 Differentiate f(x)=(x^2 + 1)/(x - 1).
- ZW-QUOTIENT-RULE-005 Differentiate f(x)=(e^x)/(x).
- ZW-QUOTIENT-RULE-006 Differentiate f(x)=(x^2)/(x^2 + 1).
- ZW-QUOTIENT-RULE-007 According to the quotient rule, what appears in the denominator of ((f)/(g))'?
- ZW-QUOTIENT-RULE-008 Compute f'(1) if f(x)=(x^3)/(x+2).