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 Notation:
Note the German scientist Gottfried Wilhem Leibniz (1646-1716) introduce the following notation: df/dx .
Note the French mathematician Joseph Louis Lagrange (1736-1813) introduce the “prime” notation f ‘(x) .
LISTS OF ELEMENTARY DERIVATIVES:
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List of some mathematic formulas here: Derivative, Integral, and more…
EXAMPLE 1: the general form is: (u n )‘ = n * u‘ * u n – 1
| Let us find the derivative of f(x) = 2 x 3
Solution: f‘(x) = ( 2 x 3 )‘ f‘(x) = 3 *( 2 x )‘*( x ) 3 – 1 f‘(x) = 6 ( x ) 2 |
EXAMPLE 2: the general form is: (u * v )‘ = u‘ v + v‘ u
| Let us find the derivative of f(x) = 2xcos(x)
Solution: f‘(x) = [ 2 x * cos(x) ]‘ f‘(x) = 2 [ x‘ cos(x)) + cos(x)‘ x ] f‘(x) = 2 [ 1 cos(x)) + (-sin(x)) x ] f‘(x) = [ 2 cos(x)) + 2x(-sin(x)) ] f‘(x) = 2 cos(x)) – 2xsin(x) |