Uploaded March 2021 | Updated September 2026, 1 hour ago

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If you're studying for a Calculus exam, then this video is for you! In this video we go over three examples of finding the derivative using the limit definitions. There is an easy, medium, and hard example of find the derivative of a function using the limit definition.

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The Easy example starts at 0:00
f(x) = x^3 + 2x.

The Medium example starts at 4:25
f(x) = 1/(x^2+1).

The Hard example starts at 8:29
f(x) = x/sqrt(x+1)
Note that we can cancel out a factor of x from the numerator and denominator at the end to get the answer you'd get when checking your answer with the quotient rule.


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