(\partial)/(\partial x)(0.5ln(x)+0.5ln(y))

Lösung

\frac{\partial}{\partial x} (0.5 ln (x) + 0.5 ln (y))

\frac{0.5}{x ^{\frac{1}{2}} x}

Schritte zur Lösung

\frac{\partial}{\partial x} (0.5 ln (x) + 0.5 ln (y))

Vereinfache

0.5 ln (x) + 0.5 ln (y) : ln (x^{0.5} y^{0.5})

= \frac{\partial}{\partial x} (ln (x^{0.5} y^{0.5}))

Behandle

y

als Konstante

Wende die Kettenregel an:

\frac{1}{x ^{0.5} y ^{0.5}} \frac{\partial}{\partial x} (x^{0.5} y^{0.5})

= \frac{1}{x ^{0.5} y ^{0.5}} \frac{\partial}{\partial x} (x^{0.5} y^{0.5})

\frac{\partial}{\partial x} (x^{0.5} y^{0.5}) = \frac{0.5 y ^{\frac{1}{2}}}{x}

= \frac{1}{x ^{0.5} y ^{0.5}} \cdot \frac{0.5 y ^{\frac{1}{2}}}{x}

Vereinfache

\frac{1}{x ^{\frac{1}{2}} y ^{\frac{1}{2}}} \cdot \frac{0.5 y ^{\frac{1}{2}}}{x} : \frac{0.5}{x ^{\frac{1}{2}} x}

= \frac{0.5}{x ^{\frac{1}{2}} x}

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