How can I apply derivation in computer???

 

I need to build an algorithm to do this.

 

There is a default method to derivation, but I dont know.

Symbolically or numerically? Numerically, the simplemost implementation is [math] f'(x) = (f(x+dx) - f(x))/dx [/math] with a relatively small variable/constant dx.

Have the user input an equation and parse it. The calculus part would be the easiest the hard part would be simplifying it (eg algebra).

Depends on the equation they input. If it's something that requires the quotient rule or something nasty like that it might be a bit difficult.