# differentiation question

Discussion in 'Mathematics' started by fudgesweets, Jun 18, 2011.

1. ### fudgesweetsNew commenter

I have been trying a step paper and was wondering,

d / du [dy/dx]= d / dx [dy/du]

is it correct to say the above is true?

2. ### fudgesweetsNew commenter

I have been trying a step paper and was wondering,

d / du [dy/dx]= d / dx [dy/du]

is it correct to say the above is true?

3. ### ResourceFinder

Seems reasonable but I am not sober so who knows

Would one say d2y by dxdu

4. ### Joslan

From my experience, I'd say it is correct to say that, since it boils down to differentiating y with respect to 2 independent variables x and u. Thus, it shouldn't make any difference with whichever of the two you decide to start with.

5. ### Polecat

With suitably generous conditions put on the functions being differentiated, this is known as the mixed derivative theorem. You have to work rather hard to find a bizarre function as a counterexample if the conditions are relaxed.

6. ### D Franklin

In the context of a STEP paper, I'd be nervous about assuming u and x are independent. (Not because STEP would be particularly tricky about u and x, but because I'd think the most likely way this came about was from some kind of substitution u = f(x)).

I don't think I've ever seen a STEP question that was supposed to be solved by differentiating w.r.t. two different variables.

7. ### Joslan

Of course D franklin, I totally agree with you!! There should be no reason to assume in mathematics especially at this level, I would imagine the complete question would have the elements for the student to decide if the variables are independent or not. I have actually seen a differentiation question in STEP of the form y=ue^x (subquestion) where u is a function of x. In this particular case, it doesn't really matter which variable you start differentiating with. In any case, there is no basis to generalise the assertion that d/du(dy/dx) is always the same as d/du(dy/dx)

8. ### D Franklin

Sure, you get lots of questions with u dependent on x (or vice versa). But I don't think I've ever seen a genuine "two indep variables" differentiation question (one where you could justifiably use \frac).Without that, I don't think the identity the OP wishes to assume is valid.
(Of the several hundred questions I've done, I think I recall one question where you might reasonably want to diff under the integral sign, but even then it was far from necessary).