Are any of these solutions correct?
-5(6x - 1)^-7/6
7(6x - 1)^-5/6
7(6x - 1)^-13/6
-5(6x - 1)^-11/6
2007-01-27 02:45:59 · 6 answers · asked by Doug 2 in Science & Mathematics ➔ Mathematics
f(x) = (6x-1)^7/6
f'(x) = (7/6)(6x-1)^1/6 * (6)
f'(x) = 7(6x-1)^1/6
f''(x) = (1/6)(7)(6x-1)^-5/6 *(6)
f''(x) = 7(6x-1)^-5/6
2007-01-27 02:53:32 · answer #1 · answered by seah 7 · 2⤊ 0⤋
f(x) = (6x - 1)^(7/6)
To find the first derivative, we use the power rule and then the chain rule. Note that the derivative of the inside (6x - 1) is 6.
f'(x) = (7/6) (6x - 1)^(1/6) {6)
Simplifying this, the 6 will merge with the (7/6) into 7.
f'(x) = 7(6x - 1)^(1/6)
Now, we get the second derivative.
f''(x) = 7(1/6) (6x - 1)^(-5/6)
Merging the 7 and the 1/6, we get
f''(x) = (7/6) (6x - 1)^(-5/6)
2007-01-27 02:50:03 · answer #2 · answered by Puggy 7 · 1⤊ 0⤋
the 2nd one, 7(6x - 1)^-5/6
the first deriv ends up being 7(6x-1)^1/6
so then the 2nd deriv is 7(6x - 1)^-5/6
*** on the answer above, he forgot the multiply by the deriv of the inside, which would be 6, so 7*(1/6)*6 is just 7
2007-01-27 02:50:25 · answer #3 · answered by kingsmansoysauce 2 · 2⤊ 0⤋
f'(x) = (7 / 6) * 6 * (6x - 1) ^ (1 / 6) = 7 * (6x - 1) ^ (1 / 6)
f''(x) = (7 / 6) * 6 * (6x - 1) ^ (-5 / 6) = 7 * (6x - 1) ^ (-5 / 6)
Your second answer is right.
2007-01-27 02:54:49 · answer #4 · answered by Shashi 2 · 1⤊ 0⤋
f(x) =(6x - 1)^7/6.
f ' (x) =(7/6) *(6x - 1) ^(1/6) *6
= 7 ( 6x - 1)^(1/6)
f'' (x) = 7 (1/6) (6x - 1) ^( - 5/6) * 6.
= 7(6x - 1) ^(- 5/6) Answer
2007-01-27 03:04:39 · answer #5 · answered by Anonymous · 0⤊ 0⤋
f(x) = (6x - 1)^7/6
rule: du/dy (u)^a = a du (u)^(a-1)
f'(x) = 7/6 * 6(6x - 1)^(7/6 - 1)
f'(x) = 7(6x - 1)^(1/6)
f''(x) = 7*(1/6)*6(6x - 1)^(1/6-1)
f''(x) = 7 (6x- 1)^(-5/6)
so the second one is correct
2007-01-27 02:51:58 · answer #6 · answered by Anonymous · 1⤊ 0⤋