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

2 Answers
Aug 7, 2016

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

Explanation:

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

Feb 18, 2017

The answer is 0.

Explanation:

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