(d^4)/(dx^4)(e^{2/x})

Lösung

\frac{d ^{4}}{d x ^{4}} (e^{\frac{2}{x}})

- \frac{2 ( - 24 e ^{\frac{2}{x}} x ^{3} - 72 e ^{\frac{2}{x}} x ^{2} - 48 e ^{\frac{2}{x}} x - 8 e ^{\frac{2}{x}} )}{x ^{8}}

Schritte zur Lösung

\frac{d ^{4}}{d x ^{4}} (e^{\frac{2}{x}})

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

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

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

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

\frac{d}{d x} - \frac{2 ( - 2 e ^{\frac{2}{x}} - 2 e ^{\frac{2}{x}} x )}{x ^{4}} = - \frac{2 ( 6 e ^{\frac{2}{x}} x ^{2} + 4 e ^{\frac{2}{x}} + 12 e ^{\frac{2}{x}} x )}{x ^{6}}

= \frac{d}{d x} - \frac{2 ( 6 e ^{\frac{2}{x}} x ^{2} + 4 e ^{\frac{2}{x}} + 12 e ^{\frac{2}{x}} x )}{x ^{6}}

\frac{d}{d x} - \frac{2 ( 6 e ^{\frac{2}{x}} x ^{2} + 4 e ^{\frac{2}{x}} + 12 e ^{\frac{2}{x}} x )}{x ^{6}} = - \frac{2 ( - 24 e ^{\frac{2}{x}} x ^{3} - 72 e ^{\frac{2}{x}} x ^{2} - 48 e ^{\frac{2}{x}} x - 8 e ^{\frac{2}{x}} )}{x ^{8}}

= - \frac{2 ( - 24 e ^{\frac{2}{x}} x ^{3} - 72 e ^{\frac{2}{x}} x ^{2} - 48 e ^{\frac{2}{x}} x - 8 e ^{\frac{2}{x}} )}{x ^{8}}

\int 3 x e^{7 x} d x

(y - (x^{2} + y^{2})) d x - x d y = 0

\frac{\partial}{\partial y} (ln (x + y + z))

in v erse l a pl a ce \frac{5 e ^{- s}}{s + 1}

\int_{0}^{3} π (x)^{2} d x