How do you find the derivative of #0# using the limit definition?

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Answer 1 · 2016-08-07T17:58:41

The derivative of zero is zero. This makes sense because it is a constant function.

Limit definition of derivative:

#f'(x) = lim_(hrarr0) (f(x+h) - f(x))/h#

Zero is a function of x such that

#f(x) = 0# #AA x#

So #f(x+h) = f(x) = 0#

#f'(x) = lim_(hrarr0)(0-0)/h = lim_(hrarr0) 0 = 0#

Answer 2 · 2017-02-18T04:33:42

The answer is 0.

#f'(x) = lim_(h->0) ((0-0)/h) = lim_(h->0) 0 = 0 #