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
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)
-------------------
You have correctly taken the log of both sides of the equation.
----------------------
Assuming you mean log and not ln, remember that the derivative of
ln(u) = 1/u u' where u' is the derivative wrt x
-----------------
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'
-------------------------
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.
======================
Cheers,
Stan H.
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