If S(x)= (inverse) f(x), then S'(x)=
That is an inverse, not an exponent of -1, the last person who tried to answer this didn't understand that.
How do I find the derivative of (inverse) f(x), when I don't know what f(x) is equal to? Are there any rules I can follow?
The back of the book explains,
f(S(x)) = x --> f ' (S(x)) x S'(x) = 1.
I don't recall learning any rule like this, will someone please explain this to me?
I need help finding the derivative of an inverse function?
2013-03-01 4:30 pm
回答 (1)
2013-03-01 5:43 pm
✔ 最佳答案
If f and S are inverse functions, thenf(S(x)) = S(f(x)) = x.
Thus,
df(S(x))/dx = dx/dx = 1
= df(S(x))/dS(x) * dS(x)/dx (chain rule).
Therefore, dS(x)/dx = 1 / df(S(x))/dS(x).
參考: Definition of Inverse Function: http://www.regentsprep.org/Regents/math/algtrig/ATP8/inverselesson.htm
Derivatives of Inverse Functions: http://oregonstate.edu/instruct/mth251/cq/Stage6/Lesson/inverseDeriv.html
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原文連結 [永久失效]:
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