derivative of y^2(6-2x)

Lösung

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

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

Schritte zur Lösung

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

Wende die Produktregel an:

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

f = y^{2}, g = 6 - 2 x

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

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

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

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

Vereinfache

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

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