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 125–128 solve the differential equation.

127. yy' = sec(y²)sec²(x)

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

15. y = sin⁻¹√(1-u²), 0<u<1

118. A particle is traveling upward and to the right along the curve y=ln(x). Its x-coordinate is increasing at the rate (dx/dt)=√x m/sec. At what rate is the y-coordinate changing at the point (e², 2)?

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)

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

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