Last one...I keep getting stuck on it... find the derivative of?

Question

ln t / (4+ Ln t)

I keep getting stuck at (4/ ln t) / (4 + ln t) ^2... I cannot figure out how to simplify further

Answer 1

f(t) = ln t / (4 + ln t)

Use the quotient rule...

f'(t) = [ (4 + ln t)/t - lnt / t] / (4 + ln t)²
f'(t) = [4 + ln t - ln t] / [t (4 + ln t)² <-- factor out a 1/t and place in denominator

f'(t) = 4 / [t (4 + ln t)²

there you go!

Answer 2

[(4 + ln t) * (1/t) - ln t*(1/t) ] / (4 + ln t)^2

[ (4/t) + ((ln t)/t) - (ln t/t)) ] / (4 + ln t)^2

(4/t) / (4 + ln t)^2

Answer 3

y=ln t / (4+ Ln t)

y'=[(1/t)(4+lnt)-(0+1/t)(lnt)]/(4+lnt)^2

y'=4/[t * (4+lnt)^2]

Answer 4

use d(f/g) = (f'g - fg')/g^2, it becomes

[(lnt)'(4+lnt) - lnt(4+lnt)]/(4+lnt)^2 ..

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

4/t (4+lnt)^2 ...