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Beliebt Rechnen >

derivative of e^{x/((x-6)})

Lösung

\frac{d}{d x} (e^{\frac{x}{( x - 6 )}})

Lösung

- \frac{6 e ^{\frac{x}{x - 6}}}{( x - 6 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (e^{\frac{x}{( x - 6 )}})

Wende die Kettenregel an:

e^{\frac{x}{x - 6}} \frac{d}{d x} (\frac{x}{x - 6})

= e^{\frac{x}{x - 6}} \frac{d}{d x} (\frac{x}{x - 6})

\frac{d}{d x} (\frac{x}{x - 6}) = - \frac{6}{( x - 6 ) ^{2}}

= e^{\frac{x}{x - 6}} (- \frac{6}{( x - 6 ) ^{2}})

Vereinfache

e^{\frac{x}{x - 6}} (- \frac{6}{( x - 6 ) ^{2}}) : - \frac{6 e ^{\frac{x}{x - 6}}}{( x - 6 ) ^{2}}

= - \frac{6 e ^{\frac{x}{x - 6}}}{( x - 6 ) ^{2}}

Graph

Beliebte Beispiele

derivative of ln(1-3/x)

\frac{d}{d x} (ln (1 - \frac{3}{x}))

limit as x approaches 2 of (x^2-2x)/x

x \to 2 lim (\frac{x ^{2} - 2 x}{x})

integral of 2/(x^3)

\int \frac{2}{x ^{3}} d x

integral of ((3x^2+6))/((x^2-2x+2)^2)

\int \frac{( 3 x ^{2} + 6 )}{( x ^{2} - 2 x + 2 ) ^{2}} d x

derivative of (3x+1ln(x-1))

\frac{d}{d x} ((3 x + 1) ln (x - 1))