1. The derivative of a function Heydar Zahedani CSU San Marcos

2. First the derivative was used, then discovered, and only then, defined.

3. Fermat, Descartes, used the above method to solve the tangent problem

4. Newton (1669)
Newton and Leibniz independently invented calculus in the latter third of the seventeenth century
Newton called our derivative a rate of flux or change and Leibniz called it the differential quotient
So the derivative was discovered

5. Leibniz (1684)

6. He claimed that any analytic function had a power series expansion
LaGrange (1797)

7. Cauchy (1823)

8. There is everywhere continuous, nowhere differentiable function.
Weierstrass (1861)

9. How did the concept of derivative develop?
Judith Grabinar

10. Caratheodory’s Theorem [ ]

11. Caratheodory’s definition of the derivative [ ]

12. Chain Rule
Caratheodory (1953)

13. Fréchet derivative
Fréchet

14. Theorem
Fréchet

15. Fréchet

16. Derivation on Algebras
Barry Edward Johnson

17. References