derivative of e^{x/((x-1)})

Lösung

\frac{d}{d x} (e^{\frac{x}{( x - 1 )}})

- \frac{e ^{\frac{x}{x - 1}}}{( x - 1 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (e^{\frac{x}{( x - 1 )}})

Wende die Kettenregel an:

e^{\frac{x}{x - 1}} \frac{d}{d x} (\frac{x}{x - 1})

= e^{\frac{x}{x - 1}} \frac{d}{d x} (\frac{x}{x - 1})

\frac{d}{d x} (\frac{x}{x - 1}) = - \frac{1}{( x - 1 ) ^{2}}

= e^{\frac{x}{x - 1}} (- \frac{1}{( x - 1 ) ^{2}})

Vereinfache

e^{\frac{x}{x - 1}} (- \frac{1}{( x - 1 ) ^{2}}) : - \frac{e ^{\frac{x}{x - 1}}}{( x - 1 ) ^{2}}

= - \frac{e ^{\frac{x}{x - 1}}}{( x - 1 ) ^{2}}

d er i v a t i v e \frac{5}{x + 6}

\frac{d}{d x} (\frac{x ^{2} 3}{4})

θ \to 0 lim (2 sec (θ))

s l o p e (0, - 1), (6, 1)

x \to 0 - lim (\frac{x ^{3} + 3}{x})