展开 x^7(a(dy)/(dx)+bx^5y^5)

解答

展开

x^{7} (a \frac{d y}{d x} + b x^{5} y^{5})

a x^{7} \frac{d y}{d x} + b x^{12} y^{5}

求解步骤

x^{7} (a \frac{d y}{d x} + b x^{5} y^{5})

使用分配律:

a (b + c) = ab + a c

a = x^{7}, b = a \frac{d y}{d x}, c = b x^{5} y^{5}

= x^{7} a \frac{d y}{d x} + x^{7} b x^{5} y^{5}

= a x^{7} \frac{d y}{d x} + b x^{7} x^{5} y^{5}

b x^{7} x^{5} y^{5} = b x^{12} y^{5}

= a x^{7} \frac{d y}{d x} + b x^{12} y^{5}

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