Determine whether the following statements are true and give an explanation or counterexample.

a. d/dx (sin^-1 x + cos^-1 x) = 0.

b. d/dx (tan^-1 x) = sec² x.

c. The lines tangent to the graph of y = sin^-1 x on the interval [-1, 1] have a minimum slope of 1.

d. The lines tangent to the graph of y = sin x on the interval [-π/2, π/2] have a maximum slope of 1.

e. If f(x) = 1/x, then (f^-1)' (x) = -1/x².