What is the derivative with respect to x of (ln x)/(cos x) is?

Question

The book list these possible solutions.

a. [(ln x)(cos x) - (1/x)(sin x)]/(ln x)^2
b. [(ln x)(sin x) + (1/x)(cos x)]/(cos x)^2
c. - [(ln x)(sin x) + (1/x)(cos x)]/(ln x)^2
d. [(1/x)(sin x) - (ln x)(cos x)]/(sin x)^2
e. none of these

Answer 1

(ln(x))/(cos(x))

(ln(x)'cos(x) - ln(x)cos(x)')/(cos(x)^2)

((1/x)cos(x) - ln(x)(-sin(x)))/(cos(x)^2)

((1/x)cos(x) + ln(x)sin(x))/(cos(x)^2)

since ((1/x)cos(x) + ln(x)sin(x))/(cos(x)^2) is the same as (ln(x)sin(x) + (1/x)cos(x))/(cos(x)^2)

ANS : B.

Answer 2

This is getting ridiculous. You don't seem to be trying and just spouting off the answers. The least you can do is try the problem and then post what you don't understand about it.