Difficult integral problem. Can any help solve?

Question

. . . . . . . . . . . . .x
If f(x) = ∫ ln (tan t) dt, what is f ''(x) ?
. . . . .. . . . . . . . . a

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These were possible solutions....

a. ln (sin x)

b. ln (cos x)

c. tan x

d. cot x

e. - tan x

f. - cot x

g. (sec x)(csc x)

h. - (sec x)(csc x)

or none of these

Answer 1

f'(x)=ln(tan t)
f"(x)=sec^2t/(tan t)
Ans: g)(sec t)(csc t)

Answer 2

I suppose you mean, f(t), then
f'(t) = ln (tan t)
f''(t) = (1/tan t) . sec^2 t = sin t . sec^3 t

I believe. If it IS f(x) use the chain rule.

Answer 3

f'(x) = ln (tan x)

f''(x) = {1 / tanx} * (sec x)^2 = sec(x) csc(x)


ans. is g