Exercise · ZW-ANTIDERIVATIVE-007 · ★★☆ Intermediate
Which is an antiderivative of \(f(x)=\sin {\left(2x \right)}\)?
Choose one option.
Show answer
- C. \(-\frac{\cos {\left(2x \right)}}{2} + C\)
Explanation
By the chain rule, \(\left(-\frac{\cos {\left(2x \right)}}{2}\right)'=\sin {\left(2x \right)}\). 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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