# 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

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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