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OpenStudy (anonymous):
g(x) = x^5 + 4x^3 + x + 1 , find (g^-1) ' (7)
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OpenStudy (anonymous):
Let \[f =g^{-1}\\ f(g(x)) =x\\ f'(g(x)) g'(x) =1\\ Notice \, that \\ g(1)=7\\ f'(g(1)) g'(1) =1\\ f'(7) = \frac 1 {g'(1)} \] Compute the last line and you are done.
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