Originally Posted by

**Paymemoney** Hi

Need help to use the Implicit Differentiation method on $\displaystyle \frac{xy}{lnx}$.

I have tried many ways to get the right answer. Below is what i have done:

$\displaystyle =\frac{\frac{dy}{dx}lnx-\frac{xy}{x}}{(lnx)^2}$

$\displaystyle \frac{\frac{dy}{dx}lnx}{(lnx)^2}-\frac{\frac{xy}{x}}{(lnx)^2}$

$\displaystyle \frac{dy}{dx}\frac{1}{lnx}=\frac{\frac{xy}{x}}{(ln x)^2}$

$\displaystyle \frac{dy}{dx}=\frac{y}{(ln)^2}-\frac{1}{lnx}$

$\displaystyle \frac{dy}{dx}=\frac{y-lnx}{(lnx)^2}$

Book's answer is $\displaystyle \frac{y-ylnx}{xlnx}$

P.S