I am new to Calculus. I know that the rate of change in some thing is called it's derivative or we differentiate something to find the rate of change in it. But while differentiating or better to say proving that if f(x)= sinx then f'(x)= cosx, we take f'(x)= lim h->0 [sin(x+h)- sinx]/h. Can you explain why? I know formulas like sin2x+ cos2x= 1 And the rest used in proving this.