Limit Definition of Derivative

Calculus students first learn the limit definition of derivatives. Using limits, we can define the slope of a tangent line to a function. And we find the slope by taking the ratio of the change in y values to the change in x values. Our intuition always tells us that if the change in x values is utterly small, we get a good approximation of the slope of the tangent line. That’s why we define the tangent line’s slope as the limit of the slope of secant lines as h approaches.

However, there is a better way to tell all those stuff in calculus; the derivative of f of x, f'(x). This math meme literally depicts calculus students when they realize they can use a simple notation for derivatives. Btw, if you want to learn calculus, you should check the online tool, Calculus Made Easy, or you can buy Spivak’s classic calculus book!

Ali Kaya


Ali Kaya

This is Ali. Bespectacled and mustachioed father, math blogger, and soccer player. I also do consult for global math and science startups.

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