Question: Show that

\[\frac{d}{dx}\left( \frac{x}{x+1} \right)=\frac{d}{dx}\left( -\frac{1}{x+1} \right)\] even though
\[\frac{x}{x+1}\ne \frac{-1}{x+1}\]

Determine whether or not this contradicts Corollary 2 of the Mean Value Theorem and explain your findings.