In Exercises 21–48, find the derivative of y with respect to the appropriate variable.
29. y=arcsec(1/t), 0<t<1

90. Find f'(0) for 

f(x) = e^(-1/x²), x≠0

   = 0, x = 0.

Solve the initial value problems in Exercises 87 and 88.

87. dy/dx = 1 + 1/x, y(1) = 3

Solve the differential equation in Exercises 9–22.

12. (dy/dx) = 3x²e^(-y)

Evaluate the integrals in Exercises 53–76.

71. ∫(from -π/2 to π/2) 2cosθ dθ/(1+(sinθ)²)

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

y = cos(e^(-θ^2))

Rewrite the expressions in Exercises 5–10 in terms of exponentials and simplify the results as much as you can.

8. cosh(3x) - sinh(3x)