® For functions u and v the following holds: u v u v ′ ′ ′ ± ± uv u v uv ′ ′ ′ u u v uv v v ′ ′ ′ = provided all are defined. ® Following are some of the standard derivatives. d nx dx (sin ) cos d dx (cos ) sin d dx =− Historical Note In the history of mathematics two names are prominent to share the credit for inventing calculus, Issac Newton ( – ) and G.W. Leibnitz ( – ).
Both of them independently invented calculus around the seventeenth century. After the advent of calculus many mathematicians contributed for further development of calculus. The rigorous concept is mainly attributed to the great MATHEMATICS mathematicians, A.L. Cauchy, J.L.Lagrange and Karl Weierstrass.
Cauchy gave the foundation of calculus as we have now generally accepted in our textbooks. Cauchy used D’ Alembert’s limit concept to define the derivative of a function. Starting with definition of a limit, Cauchy gave examples such as the limit of sin α α for α = . He wrote ( ) , f x i f x ∆ ∆ and called the limit for , i → the “function derive’e, y ′ for f ′ ( x )”.
Before , it was thought that calculus is quite difficult to teach. So calculus became beyond the reach of youngsters. But just in , John Perry and others in England started propagating the view that essential ideas and methods of calculus were simple and could be taught even in schools. F.L.
Griffin, pioneered the teaching of calculus to first year students. This was regarded as one of the most daring act in those days. Today not only the mathematics but many other subjects such as Physics, Chemistry, Economics and Biological Sciences are enjoying the fruits of calculus.