Question

Answer 1

a) \(y=f\left(x\right)=\sqrt{x^2-x+1}=\left(x^2-x+1\right)^{\dfrac{1}{2}}\)

\(y'=f'\left(x\right)=\dfrac{1}{2}\left(x^2-x+1\right)'.\left(x^2-x+1\right)^{-\dfrac{1}{2}}\)

\(y'=f'\left(x\right)=\dfrac{2x-1}{2\sqrt{x^2-x+1}}\)

\(y\left(2\right)=f'\left(2\right)=\dfrac{2.2-1}{2.\sqrt{2^2-x+1}}=\dfrac{3}{2\sqrt{3}}=\dfrac{\sqrt{3}}{2}\)

b) \(y=f\left(x\right)=\sqrt[3]{x-1}=\left(x-1\right)^{\dfrac{1}{3}}\)

\(y'=f'\left(x\right)=\dfrac{1}{2}\left(x-1\right)^{-\dfrac{2}{3}}\)

\(y'=f'\left(x\right)=\dfrac{1}{2\sqrt[3]{\left(x-1\right)^2}}\)

Đạo hàm của hàm số này không xác định tại \(x=1\)