In Exercises 57–70, use logarithmic differentiation to find the derivative of y with respect to the given independent variable.
61. y = √(θ + 3) sin θ

Indeterminate Powers and Products

Find the limits in Exercises 53–68.

66. lim (x → 0⁺) x (ln x)²

15. Find f'(2) if f(x) = e^(g(x)) and g(x) = ∫(from 2 to x) t/(1+t⁴)dt.

In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.

y = cos(e^(-θ^2))

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

64. y = 1/(t(t+1)(t+2))

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

51. lim (θ → 0) (θ - sin θ cos θ) / (tan θ - θ)

In Exercises 21–48, find the derivative of y with respect to the appropriate variable.

27. y=arccsc(x²+1)