Calculus 1: Logarithmic Differentiation

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 $y = x^{\frac{2}{x}}$

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

$y = x^{x + 1}$

Find the derivative of $y = x^{\sin{(x)}}$

Find the derivative of ${(\ln{x})}^{(\ln{(x)})}$

Use logarithmic differentiation to find the derivative of the following function

$y = \frac{(x - 1)(x + 2)(x + 3)(x - 4)}{(x + 5)(x - 3)}$