Use logarithmic differentiation to find the derivative of y

Use logarithmic differentiation to find the derivative of y with respect to x.
y=(xsqrt(x^2+6))/(x+7)^(2/3)

y=(xsqrt(x^2+6))/(x+7)^(2/3)

Thus:

ln(y) = ln(x) + 1/2 ln(x^2+6) - 2/3 ln(x+7)

So we have:

y\'/y = 1/x + x/(x^2+6) - 2/3(x+7)

Therefore:

y\' = (1/x + x/(x^2+6) - 2/3(x+7))*y = (1/x + x/(x^2+6) - 2/3(x+7))(xsqrt(x^2+6))/(x+7)^(2/3)