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Proof: $1 = 0$

Let $x = 0$. Then,

$\dfrac x x = \dfrac 0 x$
$1 = 0 \paren ?$

Proof: $\map f {-x} = \map f x \implies \map {f'} {-x} = -\map {f'} x$

$\dfrac {\d {\map f {-x} } } {\rd x} = \dfrac {\d {\map f x} } {\d x}$
$\map {f'} {-x} = -\map {f'} x$


I think you might want to explain that a little better. The notation is confusing at best. It may help to introduce an auxiliary function $\map g x = \map f {-x}$. --Dfeuer (talk) 18:19, 4 May 2013 (UTC)