Exercise · ZW-ANTIDERIVATIVE-010 · ★★☆ Intermediate
Which is an antiderivative of \(f(x)=x e^{x^{2}}\)?
Choose one option.
Show answer
- D. \(\frac{e^{x^{2}}}{2} + C\)
Explanation
By the chain rule, \(\left(\frac{e^{x^{2}}}{2}\right)'=x e^{x^{2}}\). 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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