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}

e x p an d \frac{x}{( x - 1 ) ( x - 0.7 + 0.9 j ) ( z - 0.7 - 0.9 j )}

e x p an d x ((x + 1) \cdot (x + 2))

e x p an d \frac{( s + 5 )}{s ( s ^{2} + 2 s + 10 )}

e x p an d (\frac{a}{1 - b cos ( θ )})^{2}

e x p an d f^{''} (x) (2 x + 1)^{5}