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Beliebt Rechnen >

(\partial)/(\partial x)(x^y-e^{xy})

Lösung

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

Lösung

y x^{y - 1} - e^{x y} y

Schritte zur Lösung

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

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} (e^{x y})

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

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

= y x^{y - 1} - e^{x y} y

Beliebte Beispiele

limit as x approaches+0 of (x+1)^2-x^2

x \to + 0 lim ((x + 1)^{2} - x^{2})

limit as x approaches 3-of (7-x-5)/(x-3)

x \to 3 - lim (\frac{7 - x - 5}{x - 3})

derivative of ((x+3/(x-1))^2)

\frac{d}{d x} ((\frac{x + 3}{x - 1})^{2})

derivative of 1/(x^2+2x+2)

\frac{d}{d x} (\frac{1}{x ^{2} + 2 x + 2})

(dy)/(dx)= y/x ln(y)

\frac{d y}{d x} = \frac{y}{x} ln (y)