展开 x^2dv(v-vx^2dv)

解答

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x^{2} d v (v - v x^{2} d v)

x^{2} v d v - x^{4} v d v^{2}

求解步骤

x^{2} d v (v - v x^{2} d v)

= x^{2} d v (v - x^{2} v d v)

使用分配律:

a (b - c) = ab - a c

a = x^{2} d v, b = v, c = v x^{2} d v

= x^{2} d vv - x^{2} d vv x^{2} d v

= x^{2} v d v - x^{2} x^{2} v d v d v

x^{2} x^{2} v d v d v = x^{4} v d v^{2}

= x^{2} v d v - x^{4} v d v^{2}

e x p an d \frac{2 ( 5 - 10 )}{3}

e x p an d e^{\frac{25 l n ( 63 ) - 6 ( 5 l n ( 3 ) + 6 l n ( 7 ) )}{28}}

e x p an d x^{(\frac{2}{3})}

e x p an d (7 x^{2} + 1) \cdot \frac{d ^{2} y}{d x ^{2}}

e x p an d lo g_{10} (2) (\frac{u ^{2}}{v})^{3}