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Beliebt Rechnen >

derivative of sin(y+xy-x^3)

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (sin (y)) = cos (y) \frac{d y}{d x}

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

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

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

Beliebte Beispiele

derivative of (x+1^{ln(x)})

y^{''}+2y^'=2x+7-e^{-2x}

integral from-1 to 1 of (x^2-1)^2

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