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Beliebt Rechnen >

derivative of 100(y-x^2^2+(1-x)^2)

Lösung

\frac{d}{d x} (100 (y - x^{2})^{2} + (1 - x)^{2})

Lösung

200 (y - x^{2}) (\frac{d y}{d x} - 2 x) - 2 (1 - x)

Schritte zur Lösung

\frac{d}{d x} (100 (y - x^{2})^{2} + (1 - x)^{2})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (100 (y - x^{2})^{2}) + \frac{d}{d x} ((1 - x)^{2})

\frac{d}{d x} (100 (y - x^{2})^{2}) = 200 (y - x^{2}) (\frac{d y}{d x} - 2 x)

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

= 200 (y - x^{2}) (\frac{d y}{d x} - 2 x) - 2 (1 - x)

Beliebte Beispiele

limit as x approaches 0 of x/(-x)

x \to 0 lim (\frac{x}{- x})

integral of (x^2+1/4 y^2+3)

\int (x^{2} + \frac{1}{4} y^{2} + 3) d x

(dy)/(dt)=0.03y+3600

\frac{d y}{d t} = 0.03 y + 3600

(\partial)/(\partial x)(x^{3/2})

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integral of e^{bx}

\int e^{b x} d x