Answer :

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.

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