(e^{1/x}-(e^{1/x})/x-(5e^{1/x})/(x^2))^'

Lösung

(e^{\frac{1}{x}} - \frac{e ^{\frac{1}{x}}}{x} - \frac{5 e ^{\frac{1}{x}}}{x ^{2}})^{^{'}}

\frac{11 e ^{\frac{1}{x}} x + 5 e ^{\frac{1}{x}}}{x ^{4}}

Schritte zur Lösung

(e^{\frac{1}{x}} - \frac{e ^{\frac{1}{x}}}{x} - \frac{5 e ^{\frac{1}{x}}}{x ^{2}})^{'}

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= (e^{\frac{1}{x}})^{^{'}} - (\frac{e ^{\frac{1}{x}}}{x})^{^{'}} - (\frac{5 e ^{\frac{1}{x}}}{x ^{2}})^{^{'}}

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

(\frac{e ^{\frac{1}{x}}}{x})^{'} = \frac{- e ^{\frac{1}{x}} - e ^{\frac{1}{x}} x}{x ^{3}}

(\frac{5 e ^{\frac{1}{x}}}{x ^{2}})^{'} = \frac{5 ( - e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x )}{x ^{4}}

= - \frac{e ^{\frac{1}{x}}}{x ^{2}} - \frac{- e ^{\frac{1}{x}} - e ^{\frac{1}{x}} x}{x ^{3}} - \frac{5 ( - e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x )}{x ^{4}}

Vereinfache

- \frac{e ^{\frac{1}{x}}}{x ^{2}} - \frac{- e ^{\frac{1}{x}} - e ^{\frac{1}{x}} x}{x ^{3}} - \frac{5 ( - e ^{\frac{1}{x}} - 2 e ^{\frac{1}{x}} x )}{x ^{4}} : \frac{11 e ^{\frac{1}{x}} x + 5 e ^{\frac{1}{x}}}{x ^{4}}

= \frac{11 e ^{\frac{1}{x}} x + 5 e ^{\frac{1}{x}}}{x ^{4}}

t \to 0 lim ((t - 2)^{5})

y^{^{'}} = \frac{4 x ln ( 2 x )}{sin ( y )}

\frac{d}{d x} (2 e^{x} + 3 x)

\int \frac{1}{2} sin (\frac{2 π x}{5}) d x

\frac{d}{d x} ((5 x + 8)^{2})