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Câu hỏi: Nếu $\int f(x) \mathrm{d} x=\mathrm{e}^x-\sin ^2 x+C$ thì $f(x)$ bằng
A. $\mathrm{e}^x+\cos ^2 x$
B. $\mathrm{e}^x-2 \sin x$.
C. $\mathrm{e}^x+2 \sin x$
D. $\mathrm{e}^x-\sin 2 x$.
A. $\mathrm{e}^x+\cos ^2 x$
B. $\mathrm{e}^x-2 \sin x$.
C. $\mathrm{e}^x+2 \sin x$
D. $\mathrm{e}^x-\sin 2 x$.
$
\begin{aligned}
& \text { Gọ } F(x)=\int f(x) \mathrm{d} x=\mathrm{e}^x-\sin ^2 x+C \\
& \Rightarrow f(x)=F^{\prime}(x)=\left(\mathrm{e}^x-\sin ^2 x+C\right)^{\prime}=\mathrm{e}^x-2 \cdot \sin x \cdot \cos x=\mathrm{e}^x-\sin 2 x
\end{aligned}
$
\begin{aligned}
& \text { Gọ } F(x)=\int f(x) \mathrm{d} x=\mathrm{e}^x-\sin ^2 x+C \\
& \Rightarrow f(x)=F^{\prime}(x)=\left(\mathrm{e}^x-\sin ^2 x+C\right)^{\prime}=\mathrm{e}^x-2 \cdot \sin x \cdot \cos x=\mathrm{e}^x-\sin 2 x
\end{aligned}
$
Đáp án D.