In Exercises 115–126, use logarithmic differentiation or the method in Example 6 to find the derivative of y with respect to the given independent variable.
122. y = (ln x)^(ln x)

Theory and Applications

L’Hôpital’s Rule does not help with the limits in Exercises 69–76. 

Try it—you just keep on cycling. Find the limits some other way.

71. lim (x → (π/2)⁻) sec x / tan x

In Exercises 57–70, use logarithmic differentiation to find the derivative of y with respect to the given independent variable.

66. y = θsin(θ)/√(sec(θ))

Use l’Hôpital’s rule to find the limits in Exercises 7–52.

22. lim (x → 1) (x - 1) / (ln x - sin πx)

13. When is a polynomial f(x) of at most the order of a polynomial g(x) as x→∞? Give reasons for your answer.

Evaluate the integrals in Exercises 31–78.

69. ∫dy/(y√(4y²-1))

Solve the differential equation in Exercises 9–22.

13. (dy/dx) = √y cos²√y