6. Derivatives of Inverse, Exponential, & Logarithmic Functions

Use logarithmic differentiation to find the derivative of the given function.

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

Use logarithmic differentiation to find the derivative of the given function.

$y=\sqrt{\left(\frac{x+2}{x}\right)^{\frac23}\left(x^2-4\right)}$

Use logarithmic differentiation to find the derivative of the given function.

$y=\tan^{x}x$

49–55. Derivatives of tower functions (or g^h) Find the derivative of each function and evaluate the derivative at the given value of a.

g (x) = x^ In x; a = e

Find f′(1) when f(x) = x^(1/x).

49–55. Derivatives of tower functions (or g^h) Find the derivative of each function and evaluate the derivative at the given value of a.

h (x) = x^√x; a = 4

49–55. Derivatives of tower functions (or g^h) Find the derivative of each function and evaluate the derivative at the given value of a.

f (x) = (sin x)^In x; a = π/2