# logarithmic differentiation to

• Oct 23rd 2009, 05:41 AM
kashifzaidi
logarithmic differentiation to
Use logarithmic differentiation to find the derivative of the function
http://img43.imageshack.us/img43/8438/symimagecgi.gif

I am getting this as an anwers:
http://img188.imageshack.us/img188/9...teimagecgi.gif

I know this is not the right answer.

can u help me ?

Thanks
• Oct 23rd 2009, 06:52 AM
Amer
Quote:

Originally Posted by kashifzaidi
Use logarithmic differentiation to find the derivative of the function
http://img43.imageshack.us/img43/8438/symimagecgi.gif

I am getting this as an anwers:
http://img188.imageshack.us/img188/9...teimagecgi.gif

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

$\displaystyle \frac{y'}{y} = \frac{1}{2x} + 2x + \frac{5(2x)}{x^2+2}$

$\displaystyle y' = \left(\sqrt{x} e^{x^2}(x^2+2)^5\right)\left( \frac{1}{2x} + 2x + \frac{5(2x)}{x^2+2}\right)$