Google
Câu hỏi: Nếu $f\left( x \right)=\dfrac{{{4}^{x}}}{\ln 4}$ thì ${f}'\left( x+2 \right)+2{f}'\left( x-1 \right)$ bằng
A. $\dfrac{33}{2}\ln 4f\left( x \right)$.
B. $16\ln 4f\left( x \right)$.
C. $\dfrac{65}{4}\ln 4f\left( x \right)$.
D. $24\ln 4f\left( x \right)$.
A. $\dfrac{33}{2}\ln 4f\left( x \right)$.
B. $16\ln 4f\left( x \right)$.
C. $\dfrac{65}{4}\ln 4f\left( x \right)$.
D. $24\ln 4f\left( x \right)$.
Đạo hàm ${f}'\left( x \right)={{4}^{x}}$.
Suy ra ${f}'\left( x+2 \right)+2{f}'\left( x-1 \right)={{4}^{x+2}}+{{2.4}^{x-1}}={{4}^{x}}\left( 16+\dfrac{1}{2} \right)=\dfrac{33}{2}f\left( x \right)\ln 4.$
Suy ra ${f}'\left( x+2 \right)+2{f}'\left( x-1 \right)={{4}^{x+2}}+{{2.4}^{x-1}}={{4}^{x}}\left( 16+\dfrac{1}{2} \right)=\dfrac{33}{2}f\left( x \right)\ln 4.$
Đáp án A.