Bài 4 trang 51

Đề bài

Hàm số $y=\frac{x+3}{x+2}$ có đạo hàm là

A. $y^{\prime }=\frac{1}{{\left(x+2\right)}^2}$.     

B. $y^{\prime }=\frac{5}{{\left(x+2\right)}^2}$.  

C. $y^{\prime }=\frac{-1}{{\left(x+2\right)}^2}$.                       

D. $y^{\prime }=\frac{-5}{{\left(x+2\right)}^2}$.

Lời giải chi tiết

$y^{\prime }=\frac{{\left(x+3\right)}^{\prime }\left(x+2\right)-\left(x+3\right){\left(x+2\right)}^{\prime }}{{\left(x+2\right)}^2}=\frac{1.\left(x+2\right)-\left(x+3\right).1}{{\left(x+2\right)}^2}=\frac{x+2-x-3}{{\left(x+2\right)}^2}=\frac{-1}{{\left(x+2\right)}^2}$

Chọn C.