Calculus – Anti-derivative of Hyperbolic Functions

HISTORY:  Derivation is very important in mathematics especially in calculus.
Appeared by the end of the 16th century, this concept was developed during the 17th century, by a great German philosopher and scientist named Gottfried Wilhelm Leibniz (1646-1716) and also by a great English scientist and inventor named Sir Isaac Newton(1642-1727).

Leibniz N0tation:

Note the German scientist Gottfried WilhelmLeibniz (1646-1716)introduce the following notation: df/dx .
Note the French mathematician Joseph Louis Lagrange (1736-1813) introduce the “prime” notation f (x).


List of some mathematic formulas here: Derivative, Integral, and more…

EXAMPLE 1:  the general form is:[cosh(2x) ]

Find the derivative of f(x) = [cosh(2x)]

Solution:

Note*: [ ] is used to show the function. You can replace them with parentheses ( )

EXAMPLE 2:  the general form is: [sinh(5x) ]=?

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