## TomLikesPhysics Group Title I can only find derivative for x>0 , but I don't know why (according to wolfram). one year ago one year ago

1. TomLikesPhysics Group Title

mom I need to attach the equations

2. TomLikesPhysics Group Title

3. TomLikesPhysics Group Title

My f`is apparently only true for x>0 and I have no clue where I make that assumption in my differentiation.

4. Zekarias Group Title

Your f' is defined only for |R\{-6^{0.5), 6^(0.5)}, actually

5. TuringTest Group Title

how do you figure @Zekarias

6. TuringTest Group Title

f' is not defined at +/-6^(0.5), but it is for all other points as far as I see

7. TuringTest Group Title

I do see one problem which is that for -6^(0.5)<|x|0 the slope should be negative, but the derivative is positive

8. TuringTest Group Title

-6^(0.5)<|x|<0 I meant

9. TuringTest Group Title

http://www.wolframalpha.com/input/?i=plot%20y%3D(x%5E2-6)%5E(2%2F3)&t=crmtb01 you can see the slope is negative for -6^(1/2)<x<0, but the derivative would be positive as you have it

10. TomLikesPhysics Group Title

ok, so how should I take the derivative then? Without rewriting it and using the chainrule over and over?

11. TuringTest Group Title

that I'm not so sure about. I'm thinking on it.

12. TuringTest Group Title

@amistre64 any ideas here?

13. amistre64 Group Title

the derivative on the attachment looks fine; im not sure what the question is tho

14. TuringTest Group Title

http://www.wolframalpha.com/input/?i=derivative+of+y%3D%28x%5E2-6%29%5E%282%2F3%29 true I don't see wolf giving the condition that x>0

15. TuringTest Group Title

but what about the point I brought up? f' for -6^(1/2)<x<0 should be negative, but it's positive

16. amistre64 Group Title

http://www.wolframalpha.com/input/?i=derivative+cbrt%28%28x%5E2-6%29%5E2%29 i think this has more intricate workings than we think

17. amistre64 Group Title

$u=(x^2-6)^2~:~u'=4x(x^2-6)$ $D[u^{1/3}]=\frac{u^{-1/3}}{3}u'$ $D[u^{1/3}]=\frac{4x(x^2-6)}{3((x^2-6)^2)^{1/3}}$

18. amistre64 Group Title

at -1$\frac{-*-}{+}=+$

19. TuringTest Group Title

but that should not be if you look at the graph http://www.wolframalpha.com/input/?i=plot%20y%3D(x%5E2-6)%5E(2%2F3)&t=crmtb01 should be f'<0 at x=-1

20. amistre64 Group Title

notice that the function$\sqrt[3]{((x^2-6)^2)}\ne \left(\sqrt[3]{(x^2-6)}\right)^2$at all points http://www.wolframalpha.com/input/?i=%28%28x%5E2-6%29%5E2%29%5E%281%2F3%29+-+%28%28x%5E2-6%29%5E%281%2F3%29%29%5E2

21. amistre64 Group Title

the subtlties are in how we are not using the "correct" use of a derivative

22. amistre64 Group Title

the way we are used to working with exponents seems to be a misuse of notation and doesnt express the full nature of the problem http://www.wolframalpha.com/input/?i=y%3D%28%28x%5E2-6%29%5E2%29%5E%281%2F3%29%2C+y%3D+%28%28x%5E2-6%29%5E%281%2F3%29%29%5E2

23. TomLikesPhysics Group Title

So I should not rewrite the equation and just use the chainrule multiple times then to end up with the same answer as wolfram does?

24. amistre64 Group Title

correct, I would simplify it by making a substitution; then replacing those values in the end

25. TomLikesPhysics Group Title

k, thx. I will try that now.

26. TomLikesPhysics Group Title

Damn. That went well and it was pretty quick and easy too. So the first attempt did not work because I messed the exponents up?