derivative of (ln(x)(ln(3x-7)))

Lösung

\frac{d}{d x} ((ln (x)) (ln (3 x - 7)))

\frac{ln ( 3 x - 7 )}{x} + \frac{3 ln ( x )}{3 x - 7}

Schritte zur Lösung

\frac{d}{d x} ((ln (x)) (ln (3 x - 7)))

Wende die Produktregel an:

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

f = ln (x), g = ln (3 x - 7)

= \frac{d}{d x} (ln (x)) ln (3 x - 7) + \frac{d}{d x} (ln (3 x - 7)) ln (x)

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

\frac{d}{d x} (ln (3 x - 7)) = \frac{3}{3 x - 7}

= \frac{1}{x} ln (3 x - 7) + \frac{3}{3 x - 7} ln (x)

Vereinfache

\frac{1}{x} ln (3 x - 7) + \frac{3}{3 x - 7} ln (x) : \frac{ln ( 3 x - 7 )}{x} + \frac{3 ln ( x )}{3 x - 7}

= \frac{ln ( 3 x - 7 )}{x} + \frac{3 ln ( x )}{3 x - 7}

\int \frac{ln ( x + 1 )}{x + 1} d x

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

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\int (2 x^{\frac{1}{2}}) d x