Cho hàm số \(y=f\left(x\right)=\sqrt{x+2\sqrt{x}}\). Tính \(f'\left(1\right)\) .
\(\dfrac{\sqrt{2}}{2}\).\(\sqrt{2}\).\(\dfrac{\sqrt{3}}{3}\).\(\sqrt{3}\).Hướng dẫn giải:
\(y=f\left(x\right)=\sqrt{x+2\sqrt{x}}\)\(f'\left(x\right)=\frac{\left(x+2\sqrt{x}\right)'}{2\sqrt{x+2\sqrt{x}}}=\frac{1+\frac{1}{\sqrt{x}}}{2\sqrt{x+2\sqrt{x}}}=\frac{\sqrt{x}+1}{2\sqrt{x}\sqrt{x+2\sqrt{x}}}\). Suy ra \(f'\left(1\right)=\frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}\)