derivative of 5ln(x^3)

Lösung

\frac{d}{d x} (5 ln (x^{3}))

\frac{15}{x}

Schritte zur Lösung

\frac{d}{d x} (5 ln (x^{3}))

Entferne die Konstante:

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

= 5 \frac{d}{d x} (ln (x^{3}))

Wende die Kettenregel an:

\frac{1}{x ^{3}} \frac{d}{d x} (x^{3})

= \frac{1}{x ^{3}} \frac{d}{d x} (x^{3})

\frac{d}{d x} (x^{3}) = 3 x^{2}

= 5 \cdot \frac{1}{x ^{3}} \cdot 3 x^{2}

Vereinfache

5 \cdot \frac{1}{x ^{3}} \cdot 3 x^{2} : \frac{15}{x}

= \frac{15}{x}

\frac{\partial}{\partial x} (9 x e^{6 x y})

(3 x + 2 y + 1) d x - (3 x + 2 y - 1) d y = 0

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