# How do you find the derivative using limits of #g(x)=-5#?

The derivative of a constant is null. In fact using the definition of derivative:

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To find the derivative of a constant function ( g(x) = -5 ), you apply the definition of the derivative:

[ \lim_{h \to 0} \frac{g(x + h) - g(x)}{h} ]

For ( g(x) = -5 ), the function remains constant regardless of the value of ( x ). Therefore, ( g(x + h) = -5 ) and ( g(x) = -5 ). Substituting these values into the limit expression, we get:

[ \lim_{h \to 0} \frac{-5 - (-5)}{h} = \lim_{h \to 0} \frac{0}{h} = 0 ]

Hence, the derivative of ( g(x) = -5 ) with respect to ( x ) is ( 0 ).

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