it would say, sine times the natural log times e to the natural log times e to the x. caluculus
2006-11-05 05:06:44 · 7 answers · asked by al33191 1 in Science & Mathematics ➔ Mathematics
f'(x)=cosx
(f(x) =sin(ln(e^(ln(e^x)))=...=
=sin(ln((e^lne)^x))=
=sin(lne^x)=
=sinx
2006-11-05 05:13:45 · answer #1 · answered by noname3911 1 · 0⤊ 0⤋
No, it would not say that, it would say sine of the log of e to the log of e^x. Times refers only to multilpication, not to function composition. Anyway, let's simplify that function first:
f(x)=sin(ln(e^(ln(e^x)))
f(x)=sin (ln(e^x))
f(x)=sin x
f'(x) = cos x
2006-11-05 05:11:32 · answer #2 · answered by Pascal 7 · 1⤊ 0⤋
Everything else cancels, since ln(e) is 1..
you therefore get sin x.
there is no inverse of sin x that i know of...
unless f'(x) stands for the derivative? then its cos x
2006-11-05 05:20:13 · answer #3 · answered by Anonymous · 0⤊ 0⤋
This isn't as hard as it looks. remember, ln(exp(x))=x.
2006-11-05 05:09:35 · answer #4 · answered by Shadow Fish 3 · 0⤊ 0⤋
cos x.
2006-11-05 05:21:54 · answer #5 · answered by Dr. J. 6 · 0⤊ 0⤋
f'(x) = cos(x)
2006-11-05 05:12:23 · answer #6 · answered by J 6 · 0⤊ 0⤋
f'(x) = cos(x)
2006-11-05 05:08:55 · answer #7 · answered by ? 7 · 1⤊ 0⤋