1. ## logarithmic differentiation to

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

2. Originally Posted by kashifzaidi
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

$\ln (xy) = \ln x + \ln y$

Ok

$y=\sqrt{x} e^{x^2}(x^2+2)^5$

$\ln y = \ln \left(\sqrt{x} e^{x^2} (x^2+2)^5\right)$

$\ln y = \ln \sqrt{x} + \ln e^{x^2} + \ln (x^2+2)^5$

$\ln y = \frac{\ln x}{2} + x^2 + 5\ln (x^2+2)$

now derive

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

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