In Exercises 25–30, use logarithmic differentiation to find the derivative of y with respect to the appropriate variable.
25. y = 2(x² + 1)/√(cos 2x)

112. True, or false? Give reasons for your answers.

a. 1/x⁴ = O(1/x² + 1/x⁴)

In Exercises 1–24, find the derivative of y with respect to the appropriate variable.

5. y = ln(sin²θ)

In Exercises 1–24, find the derivative of y with respect to the appropriate variable.

13. y = (x+2)^(x+2)

In Exercises 25–30, use logarithmic differentiation to find the derivative of y with respect to the appropriate variable.

29. y = (sin θ)^√θ

In Exercises 25–30, use logarithmic differentiation to find the derivative of y with respect to the appropriate variable.

27. y = (((t+1)(t-1))/((t-2)(t+3)))^5, t>2

111. True, or false? Give reasons for your answers.

c. x = o(x + ln(x))