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Beliebt Rechnen >

derivative of x^{-1}ln(x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x^{- 1}, g = ln (x)

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

y^{^{'}} = y (x y^{4} + 4)

derivative of (xy/(sqrt(xy)))

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

derivative of 6sin^2(x)

\frac{d}{d x} (6 sin^{2} (x))

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integral of sqrt(16-r^2)r

\int 16 - r^{2} r d r