derivative y=(7ln(x))/(3x+4)

Lösung

ableitung von

y = \frac{7 ln ( x )}{3 x + 4}

\frac{7 ( 3 x + 4 - 3 x ln ( x ) )}{x ( 3 x + 4 ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{7 ln ( x )}{3 x + 4})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 7 \frac{d}{d x} (\frac{ln ( x )}{3 x + 4})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= 7 \cdot \frac{\frac{d}{d x} ( ln ( x ) ) ( 3 x + 4 ) - \frac{d}{d x} ( 3 x + 4 ) ln ( x )}{( 3 x + 4 ) ^{2}}

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

\frac{d}{d x} (3 x + 4) = 3

= 7 \cdot \frac{\frac{1}{x} ( 3 x + 4 ) - 3 ln ( x )}{( 3 x + 4 ) ^{2}}

Vereinfache

7 \cdot \frac{\frac{1}{x} ( 3 x + 4 ) - 3 ln ( x )}{( 3 x + 4 ) ^{2}} : \frac{7 ( 3 x + 4 - 3 x ln ( x ) )}{x ( 3 x + 4 ) ^{2}}

= \frac{7 ( 3 x + 4 - 3 x ln ( x ) )}{x ( 3 x + 4 ) ^{2}}

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