Logarithmic Differentiation Problem

For the following function, use logarithmic differentiation to find $\frac{dy}{dx}$

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

Find the derivative of the following function

$y = \sqrt{(x^2 + 1){(x - 1)}^2}$

Determine $\frac{dy}{dx}$ for the following function

$y = \sqrt{\frac{1}{x (x + 1)}}$

Use logarithmic differentiation to find the first derivative of the function

$y = x^{x + 1}$