None of the answer you gave me are right because i have four choices, your answers are not one of them. Here are the choices and one of them is the answer.
Determine the derivative of f(x) = In (7x)
(a) f' (x) = 1 / x
(b) f' (x) = x / x^2 + 7
(c) f' (x) = 1 / 2x + 7
(d) f' (x) = 14 / x
2006-06-28 07:29:28 · 14 answers · asked by mee c 1 in Science & Mathematics ➔ Mathematics
Let a be any positive number and let f(x) = ln x and g(x) = ax. Then by the chain rule and using the fact that the derivative of ln x is 1/x, we have (ln (ax))' = (f(g(x)))' = f'(g(x)) g'(x) = (1/ax) (a) = 1/x.
2006-06-28 07:42:02 · answer #1 · answered by Anonymous · 2⤊ 0⤋
1
2006-07-01 18:44:24 · answer #2 · answered by Anonymous · 0⤊ 0⤋
I'm pretty sure it's A. The derivative of the natural log is 1 of whatever times the derivative of whatever. So...
f(x) = ln (7x)
f'(x) = ( 1 / 7x ) (7) = 7 / 7x = 1 / x
2006-06-28 14:39:31 · answer #3 · answered by Anonymous · 0⤊ 0⤋
I went back and corrected my answer to 7/7x or 1/x in your last post. So I'm going with A.
2006-06-28 14:36:53 · answer #4 · answered by bequalming 5 · 0⤊ 0⤋
The answer is a) f'(x) = 1/x
Here's why:
You need to use the chain rule to find this derivative.
Let u = 7x
dy/dx = dy/du * du/dx
dy/du = 1/u
du/dx = 7
So, dy/dx = 7*(1/u), but u = 7x so the derivative is
7*(1/7x) = 7/7x = 1/x
2006-06-28 14:35:27 · answer #5 · answered by mathsmart 4 · 0⤊ 0⤋
a - f' (x) = 1 / x
2006-06-28 14:32:54 · answer #6 · answered by sm_csu 2 · 0⤊ 0⤋
a is the answer: d(ln (7x) )= 1/7x * 7= 1/x
2006-06-28 14:38:23 · answer #7 · answered by Vivek 4 · 0⤊ 0⤋
It's A
Dx ln(7x) = 1/7x * 7 = 1/x
2006-06-28 14:50:29 · answer #8 · answered by Anonymous · 0⤊ 0⤋
the answer is
(b) f (x) = x / x^2 + 7
2006-06-28 14:35:38 · answer #9 · answered by Jenny 1 · 0⤊ 0⤋
i think 3. (c) f' (x) = 1 / 2x + 7
2006-06-28 16:15:58 · answer #10 · answered by Anry 7 · 0⤊ 0⤋