Totale Differenzierbarkeit/R/xf(y)/f stetig/Aufgabe

Sei

f\colon \mathbb {R} \longrightarrow \mathbb {R}

eine Funktion. Zeige, dass die Funktion

\varphi \colon \mathbb {R} ^{2}\longrightarrow \mathbb {R} ,\,(x,y)\longmapsto xf(y),

genau dann im Punkt ${}(0,0)$ total differenzierbar ist, wenn ${}f$ in ${}0$ stetig

ist.

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