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Beliebt Rechnen >

derivative of-x^2y^2

Lösung

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

Lösung

- 2 x y^{2} - 2 x^{2} y \frac{d y}{d x}

Schritte zur Lösung

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

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{d}{d x} (x^{2} y^{2})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{2}, g = y^{2}

= - (\frac{d}{d x} (x^{2}) y^{2} + \frac{d}{d x} (y^{2}) x^{2})

\frac{d}{d x} (x^{2}) = 2 x

\frac{d}{d x} (y^{2}) = 2 y \frac{d y}{d x}

= - (2 x y^{2} + 2 y \frac{d y}{d x} x^{2})

Vereinfache

- (2 x y^{2} + 2 y \frac{d y}{d x} x^{2}) : - 2 x y^{2} - 2 x^{2} y \frac{d y}{d x}

= - 2 x y^{2} - 2 x^{2} y \frac{d y}{d x}

Beliebte Beispiele

limit as x approaches 1-of 3x-2

x \to 1 - lim (3 x - 2)

integral of (x^2)/2 1/x

\int \frac{x ^{2}}{2} \frac{1}{x} d x

xe^y(dy)/(dx)+e^y=e^x

x e^{y} \frac{d y}{d x} + e^{y} = e^{x}

derivative of e^{-x/2}sin((sqrt(3)/2 x))

\frac{d}{d x} (e^{- \frac{x}{2}} sin (\frac{3}{2} x))

derivative 0.5x^34^x

d er i v a t i v e 0.5 x^{3} 4^{x}