Use logarithmic differentiation to find the derivative of $y = (1 +\frac1x)^{2x}$ Can someone guide me through solving this problem? 
$$\dfrac{\mathrm d}{\mathrm dx}\left(1 +\dfrac1x\right)^{2x}$$

Take logs on both sides and differentiate,
\begin{align}
y &=\left(1+\frac{1}{x}\right)^{2x}\\
\ln y &=2x \ln \left(1+\frac{1}{x}\right)\\
\frac{\frac{dy}{dx}}{ y} &=2 \ln \left(1+\frac{1}{x}\right)-2 x\frac{\frac{1}{x^2}}{1+\frac{1}{x}} \\
\frac{dy}{dx} &=2 y\ln \left(1+\frac{1}{x}\right)-2 yx\frac{\frac{1}{x^2}}{1+\frac{1}{x}} 
\end{align}
and you can substitute in for $y$ and simplify.
