You can't, perfectly. Information is lost. Taking the derivative of any constant is 0, so it is impossible to integrate and work out any constant terms that were part of the original.
(x+2)^2 has a constant term -- writing it another way, as x^2 + 4x + 4, you can see that clearly. After taking the derivative, all information about that constant term is lost. It was a 4, but from the derivative you can't tell if it was a 23 or a 7 or 2.1 billion. So no, you can't get back to (x+2)^2 from knowing the derivative is 2x + 4. Because it could have been x^2 + 4x + 3.14159 instead of x^2 + 4x + 4.
Now, if you have additional information, you can compute the constant factor. For instance, sometimes you are given the intercept or somesuch.
Posts: 15770 | Registered: Dec 2001
| IP: Logged |
quote:Originally posted by Blayne Bradley: okay so if I have f(x)=(x+2)^2
then f'(x) = 2*(x+2)* (dx/dy) x+2 which is 1
so f'(x) = 2x+4
You've lost me completely.
What is y? What variable are you differentiating with respect to?
what is 1?
Aside from that, the answer fugu and Phanto have given you is accurate.
You loose information when you take a derivative, that's why you have to add in an arbitrary constant when you integrate. In order to recover the original function by integrating a derivative, you have to have more information. Typically, you have to know the value of the initial function at some point.
Posts: 12591 | Registered: Jan 2000
| IP: Logged |