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

Lösung

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

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

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

\frac{d}{d x} (a^{x^{2}})

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