In Exercises 7–38, find the derivative of y with respect to x, t, or θ, as appropriate.
27. y = θ(sin(lnθ) + cos(lnθ))

5. e^(2t)-3e^t = 0

Evaluate the integrals in Exercises 97–110.

103. ∫₁⁴ (ln 2 · log₂x / x) dx

130. Use the identity arccot(u)=π/2 - arctan(u) to derive the formula for the derivative of arccot(u) in Table 7.4 from the formula for the derivative of arctan(u).

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

35. lim (x → 0⁺) ln(x² + 2x) / ln x

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

23. y = (x²+1)sech(ln x)

(Hint: Before differentiating, express in terms of exponentials and simplify.)

77. The region in the first quadrant bounded by the coordinate axes, the line y=3, and the curve x=2/√(y+1) is revolved about the y-axis to generate a solid. Find the volume of the solid.