(\partial)/(\partial x)(9ln(8x^2+y^3))

Lösung

\frac{\partial}{\partial x} (9 ln (8 x^{2} + y^{3}))

\frac{144 x}{8 x ^{2} + y ^{3}}

Schritte zur Lösung

\frac{\partial}{\partial x} (9 ln (8 x^{2} + y^{3}))

Behandle

y

als Konstante

Entferne die Konstante:

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

= 9 \frac{\partial}{\partial x} (ln (8 x^{2} + y^{3}))

Wende die Kettenregel an:

\frac{1}{8 x ^{2} + y ^{3}} \frac{\partial}{\partial x} (8 x^{2} + y^{3})

= \frac{1}{8 x ^{2} + y ^{3}} \frac{\partial}{\partial x} (8 x^{2} + y^{3})

\frac{\partial}{\partial x} (8 x^{2} + y^{3}) = 16 x

= 9 \cdot \frac{1}{8 x ^{2} + y ^{3}} \cdot 16 x

Vereinfache

9 \cdot \frac{1}{8 x ^{2} + y ^{3}} \cdot 16 x : \frac{144 x}{8 x ^{2} + y ^{3}}

= \frac{144 x}{8 x ^{2} + y ^{3}}

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