derivative of-(13e^{1/x}/(x^2))

Lösung

\frac{d}{d x} (- \frac{13 e ^{\frac{1}{x}}}{x ^{2}})

- \frac{13 ( - e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x )}{x ^{4}}

Schritte zur Lösung

\frac{d}{d x} (- \frac{13 e ^{\frac{1}{x}}}{x ^{2}})

Entferne die Konstante:

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

= - 13 \frac{d}{d x} (\frac{e ^{\frac{1}{x}}}{x ^{2}})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= - 13 \cdot \frac{\frac{d}{d x} ( e ^{\frac{1}{x}} ) x ^{2} - \frac{d}{d x} ( x ^{2} ) e ^{\frac{1}{x}}}{( x ^{2} ) ^{2}}

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

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

= - 13 \cdot \frac{( - \frac{e ^{\frac{1}{x}}}{x ^{2}} ) x ^{2} - 2 x e ^{\frac{1}{x}}}{( x ^{2} ) ^{2}}

Vereinfache

- 13 \cdot \frac{( - \frac{e ^{\frac{1}{x}}}{x ^{2}} ) x ^{2} - 2 x e ^{\frac{1}{x}}}{( x ^{2} ) ^{2}} : - \frac{13 ( - e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x )}{x ^{4}}

= - \frac{13 ( - e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x )}{x ^{4}}

x \to 14 lim (x^{2} - 9)

a re a y = \frac{1}{x}, y = x

\int 4 x^{2} - x^{4} d x

x \to - 1 + lim (x + 2)

\frac{d x}{d t} = 8 (x^{2} + 1), x (\frac{π}{4}) = 1