derviativtive of ln[2x]?

6 ⤊

what is the derviative of ln[2x]
is it chain rule? 1/x(2x)2

2007-11-14 15:45:44 · 3 answers · asked by ineedhelpbadly 2 in Science & Mathematics ➔ Mathematics

y = ln (2x)
Let u = 2x
du/dx = 2
y = ln u
dy/du = 1 / u
dy/dx = (dy/du) (du/dx)
dy/dx = (1 / u ) (2)
dy/dx = ((1/ (2x) )(2) = 1 / x

2007-11-15 02:53:56 · answer #1 · answered by Como 7 · 4⤊ 1⤋

yes chain rule but it is 1/x

u=2x
du/dx=2
y=ln(u)
dy/du=1/u
dy/dx =dy/u * du/dx = 2/2x=1/x

2007-11-14 23:51:12 · answer #2 · answered by Anonymous · 0⤊ 1⤋

ln[2*x] = ln[2] + ln[x]
(rules of logarithms)

now you can see the derivative is 1/x

Actually, that's really weird. (but true)

2007-11-14 23:48:50 · answer #3 · answered by Stainsor 2 · 2⤊ 1⤋