find the derivative
f(t)= 3 ln t / ( 2-ln t)
answr: 6 / (t (2 - lnt)^2)
2007-08-07 21:06:58 · 5 answers · asked by biomes 1 in Science & Mathematics ➔ Mathematics
its like lg mean log in base 10
ln mean log in base e ( natural logerithum)
2007-08-07 22:02:46 · answer #1 · answered by sanjeewa 4 · 0⤊ 1⤋
ln is the natural log or log base e. the derivative of ln x = 1/x
rewrite f(t) to = 3(ln t )(2-ln t)^-1 then use the multiplication rule to get:
3[ 1/(2-ln t)t - ln t (-1/t) / (2-ln t)^2]= 6 / (t (2 - ln t)^2)
2007-08-08 04:33:09 · answer #2 · answered by 037 G 6 · 0⤊ 1⤋
ln is natural logarithm..that is log to the base e
when we simply write logt it is log to the base 10 while lnt is log to the base e
2007-08-08 04:13:43 · answer #3 · answered by renjth k 1 · 0⤊ 2⤋
just derivate it,
f'(t)= 3 ((2-lnt)(1/t)-(lnt)(0-1/t))/(2 - lnt)^2
= (3(2-lnt+lnt))/(t(2 - lnt)^2)
= 6 / (t (2 - lnt)^2)
2007-08-08 04:16:07 · answer #4 · answered by saeed 2 · 0⤊ 1⤋
natural log or log base e
2007-08-08 04:10:43 · answer #5 · answered by Jay 4 · 0⤊ 0⤋