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

$(u^v)^\prime = (e^{v\ln u})^\prime = e^{v\ln u}\cdot(v \ln u)^\prime=u^v\cdot(v^\prime\ln u+v\cdot\frac{u^\prime}{u})$
Use this.
