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What does the notation $xf(x)$ and $f_{xxx}$ or $f_{xxy}$ mean? This is a Calculation of Stability of the limit Cycle in Hopf bifurcation, and I don't know what $f_ {xxx}$ etc , means A differential equation is given by $\frac {dx} {dt}=xf (x,y)$ What does the $xf$ stand for?
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Limit of $\frac {x^c-c^x} {x^x-c^c}$ as $x \rightarrow c$ My question is: Show that $\lim_ {x \rightarrow c} \frac {x^c-c^x} {x^x-c^c}$ exists and find its value Because the limit is 0 0 I've tried using L'Hopital's rule, but every time I differentiate it I
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