Derivative of f(x) = 3/x using limit definition of derivative?
2 Answers
Explanation:
The definition of a derivative
f'(x)=lim_(h->0)(f(x+h)-f(x))/h
We want to differentiate
f'(x)=lim_(h->0)(3/(x+h)-3/x)/h
Thus
Given:
The limit definition of the derivative is:
Substitute
Multiply by 1 in the form of
Perform the multiplication:
Please observe how this simplifies the numerator by cancellation:
The limit with the cancelled factors removed:
Distribute the -3 in the numerator:
Combine like terms:
Now, we may let
Simplify: