Expert: Ahmed Salami - 9/23/2004

Question
Hello.
In general, I know what a derivation is, but I don't know how it is calculated. I know some examples; For example (x^2)'s derivation is 2x. Or (sin x)'s derivation is cos x. But in general, I don't know which way I have to use to derive a phrase.  

Answer
Hi Mojtaba,
All derivatives are found using the methods entailing the first principles. This method is the basis to which all the formulas relating to the evaluation of derivatives are derived.
I'm not sure i can explain everything on derivatives or the first principle here. I really think a good textbook would be appropriate. But just to let you know, there is a short cut formula to calculate derivatives of polynomials.
If y = ax^n  then,
dy/dx = anx^(n-1)
So for y = x^2, a = 1 and n = 2
dy/dx = (1)(2)x^(2-1)
     = 2x
Try looking at a good text to see all the ready to use formulas for other functions.
You can always get back to me.
Regards.