erweitern 3(x+y)^2(1+(dy)/(dx))

Lösung

erweitern

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

3 x^{2} + 6 x y + 3 y^{2} + 3 x^{2} \frac{d y}{d x} + 6 x y \frac{d y}{d x} + 3 y^{2} \frac{d y}{d x}

Schritte zur Lösung

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

Wende das Distributivgesetz an:

a (b + c) = ab + a c

a = 3 (x + y)^{2}, b = 1, c = \frac{d y}{d x}

= 3 (x + y)^{2} \cdot 1 + 3 (x + y)^{2} \frac{d y}{d x}

= 3 \cdot 1 \cdot (x + y)^{2} + 3 (x + y)^{2} \frac{d y}{d x}

Vereinfache

3 \cdot 1 \cdot (x + y)^{2} + 3 (x + y)^{2} \frac{d y}{d x} : 3 x^{2} + 6 x y + 3 y^{2} + 3 x^{2} \frac{d y}{d x} + 6 x y \frac{d y}{d x} + 3 y^{2} \frac{d y}{d x}

= 3 x^{2} + 6 x y + 3 y^{2} + 3 x^{2} \frac{d y}{d x} + 6 x y \frac{d y}{d x} + 3 y^{2} \frac{d y}{d x}

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e x p an d P (6, 2, - 5) Q (0, - 5, - 3)

e x p an d sin (2 (t - w))

e x p an d (3 sin (377 t) - 1.5)^{2}

e x p an d 2 sin (6) (x + \frac{π}{3})