derivative of x^{5/x}

Lösung

\frac{d}{d x} (x^{\frac{5}{x}})

5 x^{\frac{5 - 2 x}{x}} (- ln (x) + 1)

Schritte zur Lösung

\frac{d}{d x} (x^{\frac{5}{x}})

Wende Exponentenregel an:

a^{b} = e^{b l n (a)}

x^{\frac{5}{x}} = e^{\frac{5}{x} l n (x)}

= \frac{d}{d x} (e^{\frac{5}{x} l n (x)})

Wende die Kettenregel an:

e^{\frac{5}{x} l n (x)} \frac{d}{d x} (\frac{5}{x} ln (x))

= e^{\frac{5}{x} l n (x)} \frac{d}{d x} (\frac{5}{x} ln (x))

\frac{d}{d x} (\frac{5}{x} ln (x)) = \frac{5 ( - ln ( x ) + 1 )}{x ^{2}}

= e^{\frac{5}{x} l n (x)} \frac{5 ( - ln ( x ) + 1 )}{x ^{2}}

Vereinfache

e^{\frac{5}{x} l n (x)} \frac{5 ( - ln ( x ) + 1 )}{x ^{2}} : 5 x^{\frac{5 - 2 x}{x}} (- ln (x) + 1)

= 5 x^{\frac{5 - 2 x}{x}} (- ln (x) + 1)

\int_{0}^{9} x e^{- x^{2}} d x

t a y l or \frac{1}{x ^{2}}, 1

\frac{\partial}{\partial x} (\frac{x ^{2}}{y} - x z)

\frac{\partial}{\partial y} (2 ln (3 x) - 4 ln (2 x y))

d er i v a t i v e \frac{3}{x ^{3}}