Function derivatives

I have some function,

int somefunction( //parameters here, let's say  int x) {
    return something  Let's say x*x+2*x+3 or does not matter
}

How do I find the derivative of this function? If I have

int f(int x) {
    retu开发者_开发问答rn sin(x);
}

after derivative it must return cos(x).

You can approximate the derivative by looking at the gradient over a small interval. Eg

const double DELTA=0.0001;
double dfbydx(int x) {
  return (f(x+DELTA) - f(x)) / DELTA;
}

Depending on where you're evaluating the function, you might get better results from (f(x+DELTA) - f(x-DELTA)) / 2*DELTA instead.

(I assume 'int' in your question was a typo. If they really are using integers you might have problems with precision this way.)

You can get the numerical integral of mostly any function using one of many numerical techniques such as Numerical ordinary Differential Equations

Look at: Another question

But you can get the integration result as a function definition with a library such as Maple, Mathematica, Sage, or SymPy