展開する 3(x+y)^2(1+(dy)/(dx))

解

展開する

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}

解答ステップ

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

分配法則を適用する:

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}

簡素化

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}