Câu hỏi:
Hàm số \(y = \dfrac{{{x^2} – 3x + 4}}{{{x^2} + x – 2}}\) có đạo hàm là:
-
A.
\(\dfrac{{4{x^2} – 12x – 2}}{{{{\left( {{x^2} + x – 2} \right)}^2}}}\) -
B.
\(\dfrac{{4{x^2} + 12x + 2}}{{{{\left( {{x^2} + x – 2} \right)}^2}}}\) -
C.
\(\dfrac{{4{x^2} – 12x}}{{{{\left( {{x^2} + x – 2} \right)}^2}}}\) -
D.
\(\dfrac{{4{x^2} – 12x + 2}}{{{{\left( {{x^2} + x – 2} \right)}^2}}}\)
Lời giải tham khảo:
Đáp án đúng: D
\(\begin{array}{l}y’ = \dfrac{{\left( {2x – 3} \right)\left( {{x^2} + x – 2} \right) – \left( {{x^2} – 3x + 4} \right)\left( {2x + 1} \right)}}{{{{\left( {{x^2} + x – 2} \right)}^2}}}\\y’ = \dfrac{{2{x^3} + 2{x^2} – 4x – 3{x^2} – 3x + 6 – 2{x^3} + 6{x^2} – 8x – {x^2} + 3x – 4}}{{{{\left( {{x^2} + x – 2} \right)}^2}}}\\y’ = \dfrac{{4{x^2} – 12x + 2}}{{{{\left( {{x^2} + x – 2} \right)}^2}}}\end{array}\)
Chọn D.
Trả lời