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

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TomLikesPhysics Group TitleBest ResponseYou've already chosen the best response.0
mom I need to attach the equations
 2 years ago

TomLikesPhysics Group TitleBest ResponseYou've already chosen the best response.0
My f`is apparently only true for x>0 and I have no clue where I make that assumption in my differentiation.
 2 years ago

Zekarias Group TitleBest ResponseYou've already chosen the best response.0
Your f' is defined only for R\{6^{0.5), 6^(0.5)}, actually
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
how do you figure @Zekarias
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
f' is not defined at +/6^(0.5), but it is for all other points as far as I see
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
I do see one problem which is that for 6^(0.5)<x0 the slope should be negative, but the derivative is positive
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
6^(0.5)<x<0 I meant
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
http://www.wolframalpha.com/input/?i=plot%20y%3D(x%5E26)%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
 2 years ago

TomLikesPhysics Group TitleBest ResponseYou've already chosen the best response.0
ok, so how should I take the derivative then? Without rewriting it and using the chainrule over and over?
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
that I'm not so sure about. I'm thinking on it.
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
@amistre64 any ideas here?
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
the derivative on the attachment looks fine; im not sure what the question is tho
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
http://www.wolframalpha.com/input/?i=derivative+of+y%3D%28x%5E26%29%5E%282%2F3%29 true I don't see wolf giving the condition that x>0
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
but what about the point I brought up? f' for 6^(1/2)<x<0 should be negative, but it's positive
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
http://www.wolframalpha.com/input/?i=derivative+cbrt%28%28x%5E26%29%5E2%29 i think this has more intricate workings than we think
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
\[u=(x^26)^2~:~u'=4x(x^26)\] \[D[u^{1/3}]=\frac{u^{1/3}}{3}u'\] \[D[u^{1/3}]=\frac{4x(x^26)}{3((x^26)^2)^{1/3}}\]
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
at 1\[\frac{*}{+}=+\]
 2 years ago

TuringTest Group TitleBest ResponseYou've already chosen the best response.0
but that should not be if you look at the graph http://www.wolframalpha.com/input/?i=plot%20y%3D(x%5E26)%5E(2%2F3)&t=crmtb01 should be f'<0 at x=1
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
notice that the function\[\sqrt[3]{((x^26)^2)}\ne \left(\sqrt[3]{(x^26)}\right)^2\]at all points http://www.wolframalpha.com/input/?i=%28%28x%5E26%29%5E2%29%5E%281%2F3%29++%28%28x%5E26%29%5E%281%2F3%29%29%5E2
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
the subtlties are in how we are not using the "correct" use of a derivative
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
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%5E26%29%5E2%29%5E%281%2F3%29%2C+y%3D+%28%28x%5E26%29%5E%281%2F3%29%29%5E2
 2 years ago

TomLikesPhysics Group TitleBest ResponseYou've already chosen the best response.0
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?
 2 years ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.2
correct, I would simplify it by making a substitution; then replacing those values in the end
 2 years ago

TomLikesPhysics Group TitleBest ResponseYou've already chosen the best response.0
k, thx. I will try that now.
 2 years ago

TomLikesPhysics Group TitleBest ResponseYou've already chosen the best response.0
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?
 2 years ago
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