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Beliebt Rechnen >

derivative y=(7ln(x))^2

Lösung

ableitung von

y = (7 ln (x))^{2}

Lösung

\frac{98 ln ( x )}{x}

Schritte zur Lösung

\frac{d}{d x} ((7 ln (x))^{2})

Vereinfache

(7 ln (x))^{2} : 49 ln^{2} (x)

= \frac{d}{d x} (49 ln^{2} (x))

Entferne die Konstante:

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

= 49 \frac{d}{d x} (ln^{2} (x))

Wende die Kettenregel an:

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

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

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

= 49 \cdot 2 ln (x) \frac{1}{x}

Vereinfache

49 \cdot 2 ln (x) \frac{1}{x} : \frac{98 ln ( x )}{x}

= \frac{98 ln ( x )}{x}

Graph

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