# How do you use the definition of a derivative to find the derivative of #f(x)=6#?

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The definition of derivative is:

So:

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To find the derivative of ( f(x) = 6 ), which is a constant function, you use the definition of a derivative:

[ f'(x) = \lim_{h \to 0} \frac{f(x + h) - f(x)}{h} ]

For the function ( f(x) = 6 ), the derivative is constant because the function does not change with respect to ( x ). Therefore:

[ f'(x) = \lim_{h \to 0} \frac{6 - 6}{h} ] [ f'(x) = \lim_{h \to 0} \frac{0}{h} ] [ f'(x) = \lim_{h \to 0} 0 ] [ f'(x) = 0 ]

So, the derivative of ( f(x) = 6 ) is ( f'(x) = 0 ).

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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