derivative of-xe^{((x+1/(x-1))})

Lösung

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

- \frac{e ^{\frac{x + 1}{x - 1}} x ^{2} - 4 e ^{\frac{x + 1}{x - 1}} x + e ^{\frac{x + 1}{x - 1}}}{( x - 1 ) ^{2}}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x, g = e^{\frac{x + 1}{x - 1}}

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

\frac{d x}{d x} = 1

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

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

Vereinfache

- (1 \cdot e^{\frac{x + 1}{x - 1}} + (- \frac{2 e ^{\frac{x + 1}{x - 1}}}{( x - 1 ) ^{2}}) x) : - \frac{e ^{\frac{x + 1}{x - 1}} x ^{2} - 4 e ^{\frac{x + 1}{x - 1}} x + e ^{\frac{x + 1}{x - 1}}}{( x - 1 ) ^{2}}

= - \frac{e ^{\frac{x + 1}{x - 1}} x ^{2} - 4 e ^{\frac{x + 1}{x - 1}} x + e ^{\frac{x + 1}{x - 1}}}{( x - 1 ) ^{2}}

\int \frac{x ^{2}}{x ^{2} - 4 x + 5} d x

\frac{d}{d x} (x + 5 e^{x})

t an g e n t x (49.7)

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

y^{^{''}} + 3 y^{^{'}} = 0, y (0) = 7, y^{^{'}} (0) = - 3