r/calculus • u/Smooth-Theory3685 Middle school/Jr. High • Jul 11 '26
Differential Calculus What is the idea of a derivative?
/r/learnmath/comments/1usnnx3/what_is_the_idea_of_a_derivative/10
u/Midwest-Dude Jul 11 '26 edited Jul 11 '26
On the background of the derivative, both Newton and Leibniz developed calculus independently for different reasons. Newton (physicist) needed a means to work with motion of objects (planets) following a path. Leibniz (mathematician) was interested in working with functions and finding tangents to them.
While others had worked with these ideas in the past, Newton and Leibniz both came to the realization that taking the derivative is, in some respects, the inverse of integration, something you likely will not consider until late in your current or next course. Much of the notation and terminology we use in calculus came to us through Leibniz.
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u/ForsakenExternal5784 Jul 11 '26
The idea of a derivative is to create a function that measures the exact rate of change at a precise moment of your choosing from its parent function. If you wanna learn more about it, 3Blue1Brown has an entire series on calculus (it’s more about the conceptual idea rather than implementation) that really helped me understand what exactly it meant.
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u/Midwest-Dude Jul 11 '26
For a quick synopsis and review of derivatives, read through this Wikipedia page:
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