Exercise · ZW-ANTIDERIVATIVE-003 · ★☆☆ Basic
Which is an antiderivative of \(f(x)=\frac{1}{x}\)?
Choose one option.
Show answer
- C. \(\ln{\left(\left|{x}\right| \right)} + C\)
Explanation
An antiderivative of f is a function whose derivative is f. Check by differentiating: \((\ln{\left(\left|{x}\right| \right)})'=\frac{1}{x}\). The other options have a different derivative.
Review the concept: Antiderivative
An antiderivative of \(f\) is a function \(F\) such that \(F^{\prime}=f\). If \(F\) is an antiderivative of \(f\), all the others on an interval differ from \(F\) by a constant.
\[F'(x)=f(x)\]
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