SOLUTION: I'm trying to find dy/dx on this question but before i can do that i have to simplify the expression using log laws.
{{{y= (x^2-8)^(1/3)(x^3+1)^(1/2)/(x^6-7x+5)}}}
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-> SOLUTION: I'm trying to find dy/dx on this question but before i can do that i have to simplify the expression using log laws.
{{{y= (x^2-8)^(1/3)(x^3+1)^(1/2)/(x^6-7x+5)}}}
I've taken
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Question 155846: I'm trying to find dy/dx on this question but before i can do that i have to simplify the expression using log laws.
I've taken logs so that log y= 1/3log(x^2-8) + 1/2log(x^3+1) - log(x^6 -7x + 5)
but i am unsure how to simplify it further.
Any assistance would be appreciated. Found 2 solutions by stanbon, Edwin McCravy:Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! I've taken logs so that log y= 1/3log(x^2-8) + 1/2log(x^3+1) - log(x^6 -7x + 5)
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You have correctly taken the log of both sides of the equation.
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Assuming you mean log and not ln, remember that the derivative of
ln(u) = 1/u u' where u' is the derivative wrt x
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But log(u) can be written as (1/ln(10))ln(u)
So the derivative of log(u) is (1/ln(10)*(1/u)u'
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Using that fact you should be able to find the derivative of your log equation:
(1/ln(10)(dy/dx) = (1/3)(1/ln(10))(1/(x^2-8)(2x) etc.
Write it all out then solve for dy/dx.
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Cheers,
Stan H.
You can put this solution on YOUR website!
I've taken logs so that log y= 1/3log(x^2-8) + 1/2log(x^3+1) - log(x^6 -7x + 5)
but i am unsure how to simplify it further.
Any assistance would be appreciated.
Be sure to take NATURAL logs, abbreviated "ln", not "log",
because "log" means COMMON log, that is, base 10 logs.
Multiply both side by
Finally you must replace y using the original
and the final answer is
Edwin
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