Given:
[tex]\lim _{\Delta x\to0}\frac{6(x+\Delta x)-6x_{}}{\Delta x}[/tex]
Solve as:
[tex]\begin{gathered} \lim _{\Delta x\to0}\frac{6x+6\Delta x-6x}{\Delta x}=\lim _{\Delta x\to0}\frac{6\Delta x}{\Delta x} \\ =6 \end{gathered}[/tex]
Hence, the required answer is 6.
