In Exercises 1–24, find the derivative of y with respect to the appropriate variable.
15. y = sin⁻¹√(1-u²), 0<u<1

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

5. y = ln(sin²θ)

In Exercises 125–128 solve the differential equation.

127. yy' = sec(y²)sec²(x)

Use l’Hôpital’s Rule to find the limits in Exercises 85–108.

104. lim(x→4) (sin²(πx))/(e^(x-4) + 3 - x)

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

23. y = arccsc(secθ), 0<θ<π/2

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 115 and 116, find the absolute maximum and minimum values of each function on the given interval.

116. y = 10x (2 - ln(x)), (0, e²]"133. Find the absolute maximum value of

f(x) = x^2 * ln(1/x)

and say where it is assumed