math 3 is here?

Question

Find the derivative of

f (t) =(3+ ln t)/(4 − ln t)

Answer 1

u= 3+lnt
u'= 1/t
v=4-lnt
v'=-1/t

[u'(v)-v'(u)]/v^2

[(1/t)(4-lnt)-((-1/t)(3+lnt))]/(4-lnt)^2

after simplifying you get

7/(t(4-ln t)^2)

Answer 2

f(t) = quotient rule the denominator is gonna be (4-ln t)^2

the numerator (4-ln t)(1/t) - (-1/t)(3+ln t) then simplifying

4/t - (ln t) / t +3/t - (ln t) / t - > 7/t -2(ln t) / t

combine its just [7/t - 2(ln t)/t]/ (4-ln t)^2

hopefully i didnt make any stupid mistakes

Answer 3

f '(t) = [(4-ln t)/(3+ln t) - (3+ln t)/(4-ln t)]/(4-ln t)^2

Answer 4

f'(t)=(3+lnt)/t(4-lnt)^2 + 1/t(4-lnt)

=(3+lnt+4-lnt)/t(4-lnt)^2

=7/t(4-lnt)^2