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Section 3-1 : The Definition of the Derivative

1. Use the definition of the derivative to find the derivative of,

\[f\left( x \right) = 6\] Show Solution

There really isn’t much to do for this problem other than to plug the function into the definition of the derivative and do a little algebra.

\[f'\left( x \right) = \mathop {\lim }\limits_{h \to 0} \frac{{f\left( {x + h} \right) - f\left( x \right)}}{h} = \mathop {\lim }\limits_{h \to 0} \frac{{6 - 6}}{h} = \mathop {\lim }\limits_{h \to 0} \frac{0}{h} = \mathop {\lim }\limits_{h \to 0} 0 = 0\]

So, the derivative for this function is,

\[\require{bbox} \bbox[2pt,border:1px solid black]{{f'\left( x \right) = 0}}\]