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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

s im pl i f y \frac{x - 5}{x}

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