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Calculus/Calculus Derivative Using The Technique of Logarithmic Differentation

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Expert: - 10/11/2008


Question
Find the derivative of
Using the technique of logarithmic differentation
y = {[(x - 3)^4 (x^2 + 1)] / (2x + 5)^3}^1/5

Answer
Isn't logarithimic differentiation where you say
ln(y) = ln({[(x - 3)^4 (x^2 + 1)] / (2x + 5)^3}^1/5)?

If it is, you have ln(y) = [4ln(x-3) + ln(x²+1) - 3ln(2x+5)]/5.
Taking the derivative gives you yy' on the left.
On the right, it gives [1/(x-3) + 2x/(x²+1) - 6/(2x+5)]/5.  

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