I thought I knew how to do logarithmic differentiation until I came across this:
$y = \sqrt{x(x+7)}$ find dy/dx by logarithmic differentiation
I was not phased by the problem and did the following work:
$\ln(y) = \ln(\sqrt{x(x+7)})$
$\ln(y) = {1\over 2}(\ln(x) + \ln(x+7))$
${1\over y}{dy\over dx} = {1\over 2}({1\over x}+{1\over x+7})$
${dy\over dx} = {y\over 2}({2x+7\over x^2+7x})$
but then found out that that was not actually what the answer was if you take dy/dx without logarithmic differentiation. What am I doing wrong? I have spent the past hour trying to figure it out with no luck.