Google
Câu hỏi: Biết $\int{f\left( x \right) \text{d}x={{\text{e}}^{x}}+\sin x+C}$. Mệnh đề nào sau đây đúng?
A. $f\left( x \right)={{\text{e}}^{x}}-\sin x$.
B. $f\left( x \right)={{\text{e}}^{x}}-\cos x$.
C. $f\left( x \right)={{\text{e}}^{x}}+\cos x$.
D. $f\left( x \right)={{\text{e}}^{x}}+\sin x$.
A. $f\left( x \right)={{\text{e}}^{x}}-\sin x$.
B. $f\left( x \right)={{\text{e}}^{x}}-\cos x$.
C. $f\left( x \right)={{\text{e}}^{x}}+\cos x$.
D. $f\left( x \right)={{\text{e}}^{x}}+\sin x$.
Ta có: $\int{f\left( x \right) \text{d}x={{\text{e}}^{x}}+\sin x+C}$ $\Rightarrow f\left( x \right)={{\left( {{\text{e}}^{x}}+\sin x+C \right)}^{\prime }}$ $\Rightarrow f\left( x \right)={{\text{e}}^{x}}+\cos x$.
Đáp án C.