Question 155846
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.