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Beliebt Rechnen >

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

Lösung

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

Lösung

\frac{x}{y}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Kettenregel an:

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

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

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

= \frac{1}{y ^{x}} x y^{x - 1}

Vereinfache

\frac{1}{y ^{x}} x y^{x - 1} : \frac{x}{y}

= \frac{x}{y}

Beliebte Beispiele

tangent y=6xsin(x),(pi/2 ,3pi)

t an g e n t y = 6 x sin (x), (\frac{π}{2}, 3 π)

integral of x*sqrt(x^2+3)

\int x \cdot x^{2} + 3 d x

integral of x^6(x^7-3)^{3/4}

\int x^{6} (x^{7} - 3)^{\frac{3}{4}} d x

limit as x approaches 0+of (ln(1/x))^x

x \to 0 + lim ((ln (\frac{1}{x}))^{x})

derivative of 10cos(3/10 x)

\frac{d}{d x} (10 cos (\frac{3}{10} x))