derivative of ln(x^y)

Lösung

\frac{d}{d x} (ln (x^{y}))

ln (x) \frac{d y}{d x} + \frac{y}{x}

Schritte zur Lösung

\frac{d}{d x} (ln (x^{y}))

Wende die Kettenregel an:

\frac{1}{x ^{y}} \frac{d}{d x} (x^{y})

= \frac{1}{x ^{y}} \frac{d}{d x} (x^{y})

\frac{d}{d x} (x^{y}) = x^{y} (ln (x) \frac{d y}{d x} + \frac{y}{x})

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

Vereinfache

\frac{1}{x ^{y}} x^{y} (ln (x) \frac{d y}{d x} + \frac{y}{x}) : ln (x) \frac{d y}{d x} + \frac{y}{x}

= ln (x) \frac{d y}{d x} + \frac{y}{x}

\int u^{- 2} (2 u^{4} + 3 u^{2} - 2 u^{- 3}) d u

\frac{d}{d x} (\frac{3 x - 4}{2 x ^{2} + 5})

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

x \to \frac{1}{2} lim (∣ 2 x + 3 ∣)

\frac{\partial}{\partial x} (x^{6} y^{8} + 7 x^{8} y)