PhizKid said:Don't you need to find f(u) which would be going backwards from 1 / (1 + u^3), which is an antiderivative?
And why is g'(x) != f'(x^2)? I just took the derivative of both functions on each side with respect to x
Since g(x) = f(x2), then g'(x) = f'(x2) * 2xPhizKid said:We learned the Chain Rule but not sure how to apply it here. My best guess would be:
g'(x) = f'(x) * 2x
You don't need to use the chain rule again. If f'(u) = 1/(1 + u^3) then what is f'(x^2)? Just substitute u = x^2. You are simply evaluating the function defined by f'(u) = 1/(1 + u^3) at the particular value u = x^2.PhizKid said:Sorry, that's what I meant. I write it down on paper but I'm not very good at typing
So for g'(x) I have f'(x^2) * 2x
Do I have to somehow use f'(u) = 1 / (1 + u^3) in order to find the values for 'x' for f'(x^2) * 2x ? Do I need to use the Chain Rule again? If so, how would I apply it in this situation?
PhizKid said:How do you know that u = x^2 ?
An antiderivative is the inverse operation of taking a derivative. It is a function that, when differentiated, gives back the original function.
One reason is that integration can be a time-consuming process, especially for complex functions. Finding an antiderivative without integration can be a quicker and more efficient method in some cases.
The most common method is to use the rules of differentiation in reverse. This involves identifying the function's derivative and working backwards to find the original function.
No, not all functions have a simple antiderivative that can be found without using integration. Some functions may require more advanced techniques or may not have an antiderivative at all.
Yes, there are limitations. This method may not work for all functions, and it may not always give the most accurate result. It is important to check the solution by taking the derivative of the antiderivative to ensure it matches the original function.