(d^4)/(dx^4)(e^{6/x})

Lösung

\frac{d ^{4}}{d x ^{4}} (e^{\frac{6}{x}})

- \frac{6 ( - 24 e ^{\frac{6}{x}} x ^{3} - 216 e ^{\frac{6}{x}} x ^{2} - 216 e ^{\frac{6}{x}} - 432 e ^{\frac{6}{x}} x )}{x ^{8}}

Schritte zur Lösung

\frac{d ^{4}}{d x ^{4}} (e^{\frac{6}{x}})

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

= \frac{d ^{3}}{d x ^{3}} (- \frac{6 e ^{\frac{6}{x}}}{x ^{2}})

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

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

\frac{d}{d x} - \frac{6 ( - 6 e ^{\frac{6}{x}} - 2 e ^{\frac{6}{x}} x )}{x ^{4}} = - \frac{6 ( 6 e ^{\frac{6}{x}} x ^{2} + 36 e ^{\frac{6}{x}} + 36 e ^{\frac{6}{x}} x )}{x ^{6}}

= \frac{d}{d x} - \frac{6 ( 6 e ^{\frac{6}{x}} x ^{2} + 36 e ^{\frac{6}{x}} + 36 e ^{\frac{6}{x}} x )}{x ^{6}}

\frac{d}{d x} - \frac{6 ( 6 e ^{\frac{6}{x}} x ^{2} + 36 e ^{\frac{6}{x}} + 36 e ^{\frac{6}{x}} x )}{x ^{6}} = - \frac{6 ( - 24 e ^{\frac{6}{x}} x ^{3} - 216 e ^{\frac{6}{x}} x ^{2} - 216 e ^{\frac{6}{x}} - 432 e ^{\frac{6}{x}} x )}{x ^{8}}

= - \frac{6 ( - 24 e ^{\frac{6}{x}} x ^{3} - 216 e ^{\frac{6}{x}} x ^{2} - 216 e ^{\frac{6}{x}} - 432 e ^{\frac{6}{x}} x )}{x ^{8}}

d er i v a t i v e f (x) = ln (16 sin^{2} (x))

\frac{d}{d x} ((2 x^{3} - x^{2} + 6 x + 1)^{3})

d er i v a t i v e x^{2} - 9

\int_{0}^{6} 6 x + 64 d x

\int \frac{x}{( x + 1 )} d x