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Beliebt Rechnen >

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

Lösung

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

Lösung

x^{y} ln (x) - x y^{x - 1}

Schritte zur Lösung

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

Behandle

x

als Konstante

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

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

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

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

= x^{y} ln (x) - x y^{x - 1}

Beliebte Beispiele

derivative y=(x^2-7x+7)e^{(9x)/7}

d er i v a t i v e y = (x^{2} - 7 x + 7) e^{\frac{9 x}{7}}

integral from 0 to infinity of cos(x)

\int_{0}^{\infty} cos (x) d x

integral of (6x^2+8x+3)

\int (6 x^{2} + 8 x + 3) d x

y^'=8x^3e^{-2y}

y^{^{'}} = 8 x^{3} e^{- 2 y}

derivative of-e^{-(x^2/2}x)

\frac{d}{d x} (- e^{- \frac{x ^{2}}{2}} x)