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Beliebt Rechnen >

(\partial)/(\partial x)(6ln(6x^3+y^2))

Lösung

\frac{\partial}{\partial x} (6 ln (6 x^{3} + y^{2}))

Lösung

\frac{108 x ^{2}}{6 x ^{3} + y ^{2}}

Schritte zur Lösung

\frac{\partial}{\partial x} (6 ln (6 x^{3} + y^{2}))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 6 \frac{\partial}{\partial x} (ln (6 x^{3} + y^{2}))

Wende die Kettenregel an:

\frac{1}{6 x ^{3} + y ^{2}} \frac{\partial}{\partial x} (6 x^{3} + y^{2})

= \frac{1}{6 x ^{3} + y ^{2}} \frac{\partial}{\partial x} (6 x^{3} + y^{2})

\frac{\partial}{\partial x} (6 x^{3} + y^{2}) = 18 x^{2}

= 6 \cdot \frac{1}{6 x ^{3} + y ^{2}} \cdot 18 x^{2}

Vereinfache

6 \cdot \frac{1}{6 x ^{3} + y ^{2}} \cdot 18 x^{2} : \frac{108 x ^{2}}{6 x ^{3} + y ^{2}}

= \frac{108 x ^{2}}{6 x ^{3} + y ^{2}}

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