Use logarithmic differentiation to find the derivative of the function
I am getting this as an anwers:
I know this is not the right answer.
can u help me ?
Thanks
note
$\displaystyle \ln (xy) = \ln x + \ln y $
Ok
$\displaystyle y=\sqrt{x} e^{x^2}(x^2+2)^5$
$\displaystyle \ln y = \ln \left(\sqrt{x} e^{x^2} (x^2+2)^5\right)$
$\displaystyle \ln y = \ln \sqrt{x} + \ln e^{x^2} + \ln (x^2+2)^5 $
$\displaystyle \ln y = \frac{\ln x}{2} + x^2 + 5\ln (x^2+2) $
now derive
$\displaystyle \frac{y'}{y} = \frac{1}{2x} + 2x + \frac{5(2x)}{x^2+2} $
$\displaystyle y' = \left(\sqrt{x} e^{x^2}(x^2+2)^5\right)\left( \frac{1}{2x} + 2x + \frac{5(2x)}{x^2+2}\right)$