In Exercises 7–26, find the derivative of y with respect to x, t, or θ, as appropriate.
y = ∫(from 0 to lnx) sin(e^t) dt

Evaluate the integrals in Exercises 39–56.

56. ∫sec(x)dx/√(ln(sec(x)+tan(x)))

In Exercises 5 and 6, solve for t.

6. ln(t-2) = ln8 - ln(t)

Each of Exercises 1–4 gives a value of sinh x or cosh x. Use the definitions and the identity cosh²x - sinh²x = 1 to find the values of the remaining five hyperbolic functions.

4. cosh x = 13/5, x>0

Evaluate the integrals in Exercises 97–110.

109. ∫ (dx / (x log₁₀x))

Solve the differential equation in Exercises 9–22.

17. (dy/dx) = 2x(y - 1), y > 1

In Exercises 25–36, find the derivative of y with respect to the appropriate variable.

35. y = sinh⁻¹(tan x)