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Beliebt Algebra >

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

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (3 x^{2}) = 6 x

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

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

= 6 x + 2 (y + x \frac{d y}{d x}) - 2 y \frac{d y}{d x}

Beliebte Beispiele

f(t)=(cos(5t))^2

f (t) = (cos (5 t))^{2}

faktorisieren x/(x^2-5x)

f a c t or \frac{x}{x ^{2} - 5 x}

faktorisieren 4-1.3-2000x

f a c t or 4 - 1.3 - 2000 x

faktorisieren p^2+pq-pr-qr

f a c t or p^{2} + pq - p r - q r

faktorisieren (-1/(3^2))^{-3}

f a c t or (- \frac{1}{3 ^{2}})^{- 3}