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Beliebt Rechnen >

derivative of x^2-3xy+y^2

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d}{d x} (3 x y) = 3 (y + x \frac{d y}{d x})

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

= 2 x - 3 (y + x \frac{d y}{d x}) + 2 y \frac{d y}{d x}

Beliebte Beispiele

derivative of ((sqrt(x)-2)/(sqrt(x)+2))

\frac{d}{d x} (\frac{( x - 2 )}{x + 2})

y^{^{''}} + 30 y = 0

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

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

integral of (2x^3-x+0)^3*(6x^2-1)

\int (2 x^{3} - x + 0)^{3} \cdot (6 x^{2} - 1) d x

derivative of 6^{sqrt(x)}

\frac{d}{d x} (6^{x})