(\partial)/(\partial x)(sqrt(2x^3+y^2))

Lösung

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

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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