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Beliebt Rechnen >

derivative of sqrt(x)*ln(x)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = x, g = ln (x)

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

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

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

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

Vereinfache

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

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

Graph

Beliebte Beispiele

(\partial)/(\partial x)(x^{2+y^2})

\frac{\partial}{\partial x} (x^{2 + y^{2}})

integral of (15x^4)

\int (15 x^{4}) d x

derivative of (-7x^2/(2x^2-5))

\frac{d}{d x} (\frac{- 7 x ^{2}}{2 x ^{2} - 5})

derivative of-cos(5x)

\frac{d}{d x} (- cos (5 x))

integral of 7e^4

\int 7 e^{4} d x