2006-07-03 04:09:10 · 7 answers · asked by sweets 1 in Science & Mathematics ➔ Mathematics
solve by using chain method...
f'(2x)=2
g'(e^(2x))=e^(2x)
h'(ln(e^(2x)))=1/e^(2x)
therefore...
1/2(2)(e^(2x))(1/e^(2x))=1
also, ln(x) and e^(x) are inverse functions wich means
ln(x)*e^(x)=1
2006-07-03 04:19:24 · answer #1 · answered by David J 2 · 1⤊ 1⤋
1
2006-07-03 11:40:14 · answer #2 · answered by joypinkmail 2 · 0⤊ 0⤋
The natural log and e raised to a power are inverse functions, so
ln(e^n) = n
Your denominator becomes
2ln(e^2x) = 2(2x) = 4x
1/4x = (1/4) x^(-1)
The derivative will be (-1) (1/4) x^(-2), or -1/(4x²).
2006-07-03 11:16:13 · answer #3 · answered by Louise 5 · 0⤊ 0⤋
Quite easy
In e =1
and In e^n =n
so ur question can be simplified as to findin derivative of x wrt x and U very well know thts 1 !!
2006-07-03 14:30:33 · answer #4 · answered by The Game BOY ! 1 · 0⤊ 0⤋
it is 1
lne^2x = 2x
0.5*2x=x
derivative of x is =1
2006-07-03 11:39:28 · answer #5 · answered by Anonymous · 0⤊ 0⤋
we know thatln(e^x)=x
so d/dx(1/2*ln(e^2x))=1/2*d/dx(2x)=1/2*2=1
2006-07-03 12:16:10 · answer #6 · answered by sgm 1 · 0⤊ 0⤋
i think its 1. but really, why do you want to know?
2006-07-03 11:18:30 · answer #7 · answered by halcyon blue 1 · 0⤊ 0⤋