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sporus
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Homework Statement
suppose f is a differentiable function such that f(g(x)) = x and f'(x) = 1 + [f(x)]^2. Show that g'(x) = 1/(1+ x^2)
Homework Equations
The Attempt at a Solution
since f(g(x)) = x, i think that f is the inverse of g.
so f = g{inverse}
f'(x) = f'(g(x)) * g'(x) = 1 + [f(x)]^2
we are given g'(x) and f'(x), but i can't make the connection between the fact that f = g{inverse} and how it affects f'(g(x)) because that is the only missing part of the equation.