Consider the function f(x) for which f(0)=7 and f'(0)=7. Find h'(0) for th function h(x)= 1/f(x). h'(0)= please explain?
回答 (4)
2016-02-29 6:46 pm
✔ 最佳答案
since f'(x)=7, if we assume that this is a line 7=m then:y=7x+b, and since (0,7), b=7 then:
y=7x+7 making
h(x)=1/f(x) become:
h(x)=1/(7x+7)
dh/dx=-7/(7x+7)^2 and when x=0
dh/dx=-1/7
2016-02-29 6:12 pm
h(x) = 1/f(x)
Or for brevity:
h = 1/f
dh/df = -1/f²
dh/dx = (dh/df)(df/dx) (chain rule)
. . .. . .= (-1/f²)df/dx
Writing h'(x) for dh/dx, f'(x) for df/dx and f(x) for f gives:
h'(x) = (-1/f(x)²)f'(x)
For x=0
h'(0) = (-1/f(0)²)f'(0)
. . . . = (-1/7²)7
. . . . = -1/7
Or for brevity:
h = 1/f
dh/df = -1/f²
dh/dx = (dh/df)(df/dx) (chain rule)
. . .. . .= (-1/f²)df/dx
Writing h'(x) for dh/dx, f'(x) for df/dx and f(x) for f gives:
h'(x) = (-1/f(x)²)f'(x)
For x=0
h'(0) = (-1/f(0)²)f'(0)
. . . . = (-1/7²)7
. . . . = -1/7
收錄日期: 2021-04-18 14:33:36
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