what does: [d/dx](lne^3x)=
2007-03-22 17:15:57 · 5 answers · asked by GHAAD 4 in Science & Mathematics ➔ Mathematics
Since the natural logarithm function and the natural exponential function are inverses of one another,
ln(e^3x) = 3x.
So (d/dx)(ln(e^3x)) = (d/dx)(3x) = 3
2007-03-22 17:19:30 · answer #1 · answered by polymac98 2 · 2⤊ 0⤋
let y =ln(e^3x)
thus , y=3xlne=3x(1)=3x
therefore dy/dx=3
2007-03-23 00:22:37 · answer #2 · answered by llcold 2 · 1⤊ 0⤋
(d/dx) ln(e^(3x))
We can algebraically manipulate ln( e^(3x)) prior to taking the derivative. Using the log property that allows us to bring the 3x to the front, we get
ln(e^(3x)) = (3x) ln(e)
But ln(e) = 1, so we just get 3x.
(d/dx) (3x) = 3
2007-03-23 00:20:24 · answer #3 · answered by Puggy 7 · 1⤊ 0⤋
1) (lne^3x) = 3x ln(e) =3x(1)=3x
2) d/dx(3x) =3
Answer : 3
2007-03-23 00:44:40 · answer #4 · answered by frank 7 · 0⤊ 0⤋
3
ln (e^3x) = 3x
ln and e^ are inverse of each other
so deriv of 3x is 3
2007-03-23 00:20:17 · answer #5 · answered by N M 2 · 1⤊ 0⤋