展開する 6(x^2+y^2)^5(2x+2y(dy)/(dx))

解

展開する

6 (x^{2} + y^{2})^{5} (2 x + 2 y \frac{d y}{d x})

12 x^{11} + 60 x^{9} y^{2} + 120 x^{7} y^{4} + 120 x^{5} y^{6} + 60 x^{3} y^{8} + 12 x y^{10} + 12 x^{10} y \frac{d y}{d x} + 60 x^{8} y^{3} \frac{d y}{d x} + 120 x^{6} y^{5} \frac{d y}{d x} + 120 x^{4} y^{7} \frac{d y}{d x} + 60 x^{2} y^{9} \frac{d y}{d x} + 12 y^{11} \frac{d y}{d x}

解答ステップ

6 (x^{2} + y^{2})^{5} (2 x + 2 y \frac{d y}{d x})

分配法則を適用する:

a (b + c) = ab + a c

a = 6 (x^{2} + y^{2})^{5}, b = 2 x, c = 2 y \frac{d y}{d x}

= 6 (x^{2} + y^{2})^{5} \cdot 2 x + 6 (x^{2} + y^{2})^{5} \cdot 2 y \frac{d y}{d x}

= 6 \cdot 2 x (x^{2} + y^{2})^{5} + 6 \cdot 2 y (x^{2} + y^{2})^{5} \frac{d y}{d x}

簡素化

6 \cdot 2 x (x^{2} + y^{2})^{5} + 6 \cdot 2 y (x^{2} + y^{2})^{5} \frac{d y}{d x} : 12 x^{11} + 60 x^{9} y^{2} + 120 x^{7} y^{4} + 120 x^{5} y^{6} + 60 x^{3} y^{8} + 12 x y^{10} + 12 x^{10} y \frac{d y}{d x} + 60 x^{8} y^{3} \frac{d y}{d x} + 120 x^{6} y^{5} \frac{d y}{d x} + 120 x^{4} y^{7} \frac{d y}{d x} + 60 x^{2} y^{9} \frac{d y}{d x} + 12 y^{11} \frac{d y}{d x}

= 12 x^{11} + 60 x^{9} y^{2} + 120 x^{7} y^{4} + 120 x^{5} y^{6} + 60 x^{3} y^{8} + 12 x y^{10} + 12 x^{10} y \frac{d y}{d x} + 60 x^{8} y^{3} \frac{d y}{d x} + 120 x^{6} y^{5} \frac{d y}{d x} + 120 x^{4} y^{7} \frac{d y}{d x} + 60 x^{2} y^{9} \frac{d y}{d x} + 12 y^{11} \frac{d y}{d x}