How would I simplify this fraction easily? Original question : (tan(x))/(\log_e x) I used the quotient rule and got the following fraction. Fraction : ((x * sec(x)^2 * (log_e x) - tan(x))/(x))/(log_e x)

figoveck38

figoveck38

Answered question

2022-11-05

How would I simplify this fraction easily?
Original question :
tan ( x ) log e x
I used the quotient rule and got the following fraction.
Fraction :
x sec ( x ) 2 ( log e x ) tan ( x ) x log e x
apologies in advance for the fractions, i tried to put in log e x underneath the denominator of the other fraction but for some reason it wasn't working.

Answer & Explanation

sliceu4i

sliceu4i

Beginner2022-11-06Added 16 answers

Let
f ( x ) = tan x ln x
Using the Quotient Rule, we get
f ( x ) = tan x ln x tan x ln x ln 2 x = ln x cos 2 x sin x x cos x ln 2 x = x ln x sin x cos x x cos 2 x ln 2 x
on multiplying numerator and denominator by x cos 2 x.
If you prefer to split it in fractions,
f ( x ) = 1 ln x cos 2 x tan x x ln 2 x

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