derivative of x^{-2}ln(x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{- 2}, g = ln (x)

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

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

\frac{d}{d x} (ln (x)) = \frac{1}{x}

= (- \frac{2}{x ^{3}}) ln (x) + \frac{1}{x} x^{- 2}

Vereinfache

(- \frac{2}{x ^{3}}) ln (x) + \frac{1}{x} x^{- 2} : \frac{- 2 ln ( x ) + 1}{x ^{3}}

= \frac{- 2 ln ( x ) + 1}{x ^{3}}

\int_{1}^{4} \frac{x}{x ^{2} + 6 x + 13} d x

\frac{\partial}{\partial x} (arctan (3 x))

x \to \infty lim (\frac{4 x ^{6} - x}{x ^{3} + 2})

x \to \infty lim (2 x e^{- 2 x})

x \to 0 lim (\frac{7 x ^{4} - x ^{3}}{x})