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Beliebt Rechnen >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Behandle

y

als Konstante

Wende die Summen-/Differenzregel an:

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

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

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

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

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

Beliebte Beispiele

tangent 4x^2,\at x=3

t an g e n t 4 x^{2}, at x = 3

(\partial)/(\partial θ)(θ)

\frac{\partial}{\partial θ} (θ)

integral of 12x^2-sin(x)

\int 12 x^{2} - sin (x) d x

x^2y^'-2x^3e^{(-1)/x}=y

x^{2} y^{^{'}} - 2 x^{3} e^{\frac{- 1}{x}} = y

integral of 4/(x(x^2+4)^2)

\int \frac{4}{x ( x ^{2} + 4 ) ^{2}} d x