Question

find f(x).

f(x) = \frac{2x}{19 + \ln x}

Explanation:

Step1: Apply the quotient rule

The quotient rule is \((\frac{u}{v})^\prime=\frac{u^\prime v - uv^\prime}{v^2}\). Let \(u = 2x\), \(u^\prime=2\); \(v=19+\ln x\), \(v^\prime=\frac{1}{x}\).

Step2: Substitute into the quotient rule formula

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Answer:

\(f^\prime(x)=\frac{2(18+\ln x)}{(19+\ln x)^2}\)