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February 2nd, 2009, 04:09 PM   #1
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Problem with derivative

I would be really grateful if anyone could help me with this derivative:



OK, I believe I need to use the quotient rule, and I'll get something like that:



but I don't know what to do next...
StevenMx is offline  
 
February 3rd, 2009, 03:20 AM   #2
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Re: Problem with derivative

Updated my previous post
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February 3rd, 2009, 09:46 AM   #3
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Re: Problem with derivative

Quote:
Originally Posted by StevenMx

but I don't know what to do next...
First of all, your quotient rule is wrong. You add, not multiply, the two terms


Now, from trigonometry, we ought to know that:




The real question is this... do you know how to find the derivative of an inverse function?

Follow this procedure for any arbitrary inverse function...

Suppose

Then by definition of an inverse function

Find the derivative: utilizing both chain rule and implicit differentiation.

Solve for y':

Plug in your function y in terms of x:


There... thats all you need to know for an arbitrary f(x)... you can find the derivative of any f^-1.

Given that in your problem
,

we know that
and therefore









Refer back to your original problem:


Remembering your chain rules


You have to look back at good old trigonometry yet again...

and so


Plugging in:




This problem is boring me. I will quit now.
CogitoErgoCogitoSum is offline  
February 4th, 2009, 03:18 AM   #4
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Re: Problem with derivative

Thanks man I really appreciate that.
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February 4th, 2009, 04:58 AM   #5
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Re: Problem with derivative

Quote:
First of all, your quotient rule is wrong. You add, not multiply, the two terms
Actually, you subtract, not add...

d/dx ( u / v) = (u' * v - u * v') / v^2
shynthriir is offline  
February 4th, 2009, 06:56 AM   #6
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Re: Problem with derivative

Quote:
Originally Posted by shynthriir
Quote:
First of all, your quotient rule is wrong. You add, not multiply, the two terms
Actually, you subtract, not add...

d/dx ( u / v) = (u' * v - u * v') / v^2
LOL. you certainly do. Im sorry man, I totally screwed that up for you. Just change the signs.
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February 4th, 2009, 07:14 AM   #7
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Re: Problem with derivative

Don't worry man, nothing happened I changed the signs.
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