derivative f(x)=(x+2)e^{1/x}

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x + 2, g = e^{\frac{1}{x}}

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

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

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

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

Vereinfache

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

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

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

y^{^{'}} = e^{y - x}

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

d er i v a t i v e \frac{sec ( x )}{1 + sec ( x )}

\int x ln^{3} (x) d x