In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.
y = ln(e^(θ)/(1+e^θ))

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

39. lim (x → ∞) (ln 2x - ln(x + 1))

Evaluate the integrals in Exercises 39–56.

41. ∫2y dy/(y²-25)

Evaluate the integrals in Exercises 53–76.

69. ∫dx/((2x-1)√((2x-1)²-4))

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.

115. y = (x + 1)ˣ

In Exercises 13–24, find the derivative of y with respect to the appropriate variable.

21. y = ln(cosh v) - 1/2 tanh²v

82. For what values of a and b is

lim(x→0)(tan(2x/x³) + a/x² + sin(bx)/x) = 0?