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Câu hỏi: Cho $\int{\dfrac{1}{2x+1}dx}=F\left( x \right)+C$. Khẳng định nào dưới đây đúng?
A. ${F}'\left( x \right)=\dfrac{1}{2x+1}$.
B. ${F}'\left( x \right)=-\dfrac{2}{{{\left( 2x+1 \right)}^{2}}}$.
C. ${F}'\left( x \right)=\dfrac{2}{{{\left( 2x+1 \right)}^{2}}}$.
D. ${F}'\left( x \right)=\dfrac{1}{2}\ln \left( 2x+1 \right)$.
A. ${F}'\left( x \right)=\dfrac{1}{2x+1}$.
B. ${F}'\left( x \right)=-\dfrac{2}{{{\left( 2x+1 \right)}^{2}}}$.
C. ${F}'\left( x \right)=\dfrac{2}{{{\left( 2x+1 \right)}^{2}}}$.
D. ${F}'\left( x \right)=\dfrac{1}{2}\ln \left( 2x+1 \right)$.
Ta có $\int{\dfrac{1}{2x+1}dx}=F\left( x \right)+C\Rightarrow {F}'\left( x \right)=\dfrac{1}{2x+1}$.
Đáp án A.
