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derivatives of inverses again!!

ok so

f-1 '(x)=1/f'(f-1(x))

but doesnt f-1 '(x)=f'(f-1(x))???


please clear my confusion!
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realicetic
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realicetic
ok so

f-1 '(x)=1/f'(f-1(x))

but doesnt f-1 '(x)=f'(f-1(x))???


please clear my confusion!


anyone?
:smile:
Consider f(g(x))

f(g(x))' = f'(g(x))g'(x)

Let g = f-1 so f(g(x)) = f(f-1(x)) = x, so f(g(x))' = x' = 1 so

1 = f'(f-1(x))(f-1)'(x)

so (f-1)'(x) = 1 / f'(f-1(x))

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