You are Here: Home >< Maths

# Integration help watch

1. Hi, I have this question: Integrate x f'(x^2) dx. My answer should be in terms of f. What does this mean? Because I know f' of x^2 is 2x but then I'd be left with x times 2x dx which is 2x^2 dx which is (2x^3)/3? But that seems way too easy so I'm stuck...
2. Clue: think about what the differential of f(x^2) is and don't forget to use the chain rule.

Substitute in x^2 =y if you need to then remember df/dx =df/dy * dy/dx

Random note f is any arbitrary function
3. You need to tighten up your definitions a bit or mistakes will follow. f' is an abbreviation for the derivative of a single-variable function f(.) with respect to that variable. Saying "f' of x^2 is 2x" is therefore sloppy and meaningless.

Correct statements: "the derivative (with respect to x) of x^2 is 2x", "if f(x) = x^2 then the derivative of f (with respect to x) is 2x", "if f(x) = x^2 then f' = 2x"

Anyway back to your problem, what is (f(x^2))'? or d/dx [f(x^2)] if you prefer (it's the same thing).
4. Sorry but I'm still confused. I know dy/dx is f'(x) but... just don't get it :/
5. The problem is that you don't understand the chain rule. Telling you the solution won't address that.

Try to understand what the derivative of f(g(x)) is in general (the chain rule tells you!) then apply it to this case.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: October 26, 2017
Today on TSR

### Exam Jam 2018

Join thousands of students this half term

Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams