Today, not only Mathematics but many other subjects such as physics, chemistry and economics are enjoying the fruits of calculus. The credit goes to the great English Mathematician Sir Isaac Newton and the noted German Mathematician G.W. Libnitz, who independently invented calculus around seventeenth century. After the advent of calculus many mathematicians contributed for further development of mathematics. Cauchy gave the foundation of calculus. He used D' Alembert's limit concept to define the derivative of a function. He wrote

Geometrically, f'(x) is interpreted as the slope of the curve at the point (x, f(x)). The line through (x, f(x)) which has this slope is called tangent at (x, f(x)). If there is no tangent at a certain point then the function is not differentiable at that point.
* Right hand derivative of f(x) at x = x0 is denoted by f'(x0+) and is defined as
       and 
    Left hand derivative of f(x) at x = x0 is denoted by f'(x0-) and is defined as 

    If f'(x0+) = f'(x0-) then f(x) is differentiable at x = x0.
* If a function is differentiable on [a, b] then f(x) is differentiable at every 

* Every differentiable function is continuous but not the converse.
* If y = f(x) is a differentiable function such that z = f'(x) is also differentiable then the second derivative of y = f(x) is denoted by y2(x), f''(x)or and difined as

 If f'(x) = 0 at every point of a certain interval, then f(x) is constant on that interval.
* If y = f(x) satisfies the equation F (x, y) = 0 then to find , when y is differentiable,
differentiate F w.r.t. x considering y as a function of x and solve for .
* If x = f(t) and y = g(t) are two differentiable functions then 

*  Use of logarithms will be of great help in finding the derivative of the function of the form    
              (i)  y = f(x)g(x)

 If y = f(x) and z = g(x) then  
* If y = [f(x)]y then   =
* If f(x + y) = f(x).f(y) and f'(0) exists then f'(x) = f(x) f'(0).