derivative \sqrt[x]{x}

Lösung

ableitung von

x x

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

x x = e^{\frac{1}{x} l n (x)}

= \frac{d}{d x} (e^{\frac{1}{x} l n (x)})

Wende die Kettenregel an:

e^{\frac{1}{x} l n (x)} \frac{d}{d x} (\frac{1}{x} ln (x))

= e^{\frac{1}{x} l n (x)} \frac{d}{d x} (\frac{1}{x} ln (x))

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

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

Vereinfache

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

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

d er i v a t i v e - 0.6 t^{2} + 30 t

\int_{0}^{5} π (- \frac{3}{5} x + 3)^{2} d x

d er i v a t i v e \frac{t ^{3} + 3 t}{t ^{2} - 4 t + 3}

\int \frac{7}{x ( x - 7 ) ^{2}} d x

\frac{d}{d x} ((x - 100)^{3} + (x - 100)^{2} + 500)