The derivative of the function $f\left(x\right)=3x\text{ at }x=2$ is

We have,

$$\begin{gathered} f^{\mathrm{\prime }}\left(2\right)=\underset{h\to 0}{lim} \frac{f(2+h)-f\left(2\right)}{h}=\underset{h\to 0}{lim} \frac{3(2+h)-3\left(2\right)}{h} \\ =\underset{h\to 0}{lim} \frac{6+3h-6}{h}=\underset{h\to 0}{lim} \frac{3h}{h}=\underset{h\to 0}{lim} 3=3 \end{gathered}$$

The derivative of the function $f\left(x\right)=3x at x=2$ is 3.