Cho hàm số $f\left(x\right)=\sqrt{1+x} ; Tính f\left(3\right)+\left(x-3\right)f\text{'}\left(3\right)$

Giải

Ta có $$\begin{gathered} f\text{'}\left(x\right)=\frac{1}{2\sqrt{1+x}}\Rightarrow f\text{'}\left(3\right)=\frac{1}{4}\text{'}f\text{'}\left(3\right)=2 \\ Vậy f\text{'}\left(3\right)+\left(x-3\right) f\text{'}\left(3\right)=2+\frac{x-3}{4}=\frac{x+5}{4} \end{gathered}$$