Answer
\[f'\left( c \right)=0\]
Work Step by Step
\[\begin{align}
& \text{Let }f\left( x \right)=c,\text{ using the definition of the derivative} \\
& f'\left( x \right)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f\left( x+h \right)-f\left( x \right)}{h} \\
& \text{Calculate the derivative for }f\left( x \right)=c \\
& f'\left( c \right)=\underset{h\to 0}{\mathop{\lim }}\,\frac{c-c}{h} \\
& f'\left( c \right)=\underset{h\to 0}{\mathop{\lim }}\,0 \\
& f'\left( c \right)=0 \\
\end{align}\]
