2007-12-14 07:05:43 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
y = ln (4x)
Let u = 4x
du/dx = 4
y = ln u
dy/du = 1 / u
dy/dx = (1/u) (4)
dy/dx = (1 / 4x) (4)
dy/dx = 1 / x
2007-12-17 06:57:49 · answer #1 · answered by Como 7 · 3⤊ 1⤋
Use the chain rule: the derivative of ln(x), or the outside, multiplied by the derivative of the inside(4x) so that you get
(1/4x)(4)
2007-12-14 15:12:57 · answer #2 · answered by Nebuchaednezzar_2004 3 · 2⤊ 1⤋
derivative of ln(4x) = 1/4x * 4 = 1/x
2007-12-14 15:11:38 · answer #3 · answered by sv 7 · 3⤊ 1⤋
ln(4x) = ln 4 + ln x.
So the derivative of ln(4x) is just 1/x, since ln 4 is a constant.
2007-12-14 15:12:25 · answer #4 · answered by steiner1745 7 · 3⤊ 1⤋
derivative of log(ax), where a is a constant is always 1/x
in this case a =4
derivative of log(4x) = 1/x
2007-12-14 15:15:50 · answer #5 · answered by Any day 6 · 1⤊ 2⤋
y = ln (4x)
set u = 4x , then , y = ln(u)
du = 4 dx , then , du/dx = 4,
dy/dx = dy/du*du/dx
then dy/dx = 1/u * 4 = 4/u = 4/4x = 1/x
2007-12-14 15:14:11 · answer #6 · answered by Nur S 4 · 2⤊ 1⤋