Antiderivatives?

Question

I need the rules for doing antiderivatives

For ex:

f'(x) = (f(x))/(g(x))
f'(x) = (f(x))(g(x))
f'(x) = f(x) + g(x)
f'(x) = f(x) - g(x)

sorry, since it has been so long, i am not certain how to actual write them.

I tried looking it up, but didn't really have any luck, but if you can, can you send me site(s) that will show me the rules to do them.

I can do derivatives just fine, its the antiderivatives i'm not all familiar with.

i can kinda understand how to do them, but i have seen some antiderivative answers with f'(x) + C and i'm not certain where the C comes from, and thats why i wanted the websites to show me how to work them.

Answer 1

I believe the "antiderivative" you're looking for is called an "integral". They are generally more tricky to compute than derivatives, so you're gonna need to read a calculus book to learn how to do them. See the wikipedia page on integrals:
http://en.wikipedia.org/wiki/Integral

As rscanner mentioned, when you take a derivative, you throw away the constant terms, which is why you generally put a + C when you write the closed form of an integral. What is the C? You can think of it like this. If p(t) is the position of your car at time t, then p'(t), the derivative, is the speed of your car at time t.

Now suppose someone tells you that your speed is p'(t) = 2 kilometers/hour. And someone asks you where your car is after t hours. You'll be able to say "it's 2*t kilometers from where it started", but you won't be able to say exactly where the car is. The "+ C" is the "where it started" part. So you write p(t) as 2*t + C.

Answer 2

The C is a constant which all antiderivatives have. Because the derivative of C is 0 and is eliminated in the derivative.

Answer 3

"In calculus, an antiderivative, primitive or indefinite integral of a function f is a function F whose derivative is equal to f, i.e., F ′ = f. The process of solving for antiderivatives is antidifferentiation (or indefinite integration). They are also called integrals, but this usage is not universally accepted. Antiderivatives are related to definite integrals through the fundamental theorem of calculus, and provide a convenient means for calculating the integrals of many functions."