Bài tập 3 trang 43 SBT Toán 11 Tập 2 Chân trời sáng tạo - CTST

a) Ta có: $y\text{'}=20{\left(1+x^2\right)}^{19}.{\left(1+x^2\right)}^{\text{'}}$

$=20{\left(1+x^2\right)}^{19}.2x$

$=40x{\left(1+x^2\right)}^{19}$.

b) Ta có: $y^{\text{'}}=\frac{{\left(2+x\right)}^{\text{'}}\sqrt{1-x}-\left(2+x\right){\left(\sqrt{1-x}\right)}^{\text{'}}}{{\left(\sqrt{1-x}\right)}^2}$

$=\frac{\sqrt{1-x}-\left(2+x\right)\frac{{\left(1-x\right)}^{\text{'}}}{2\sqrt{1-x}}}{{\left(\sqrt{1-x}\right)}^2}$

$=\frac{\sqrt{1-x}-\left(2+x\right)\left(-\frac{1}{2\sqrt{1-x}}\right)}{\left(1-x\right)}$

$=\frac{2\left(1-x\right)+\left(2+x\right)}{2\left(1-x\right)\sqrt{1-x}}$

$=\frac{4-x}{2\left(1-x\right)\sqrt{1-x}}$.

-- Mod Toán 11 HỌC247