展开 x(3x+5vx)(v+x(dv)/(dx))

解答

展开

x (3 x + 5 vx) (v + x \frac{d v}{d x})

3 x^{2} v + 3 x^{3} \frac{d v}{d x} + 5 x^{2} v^{2} + 5 x^{3} v \frac{d v}{d x}

求解步骤

x (3 x + 5 vx) (v + x \frac{d v}{d x})

= x (3 x + 5 xv) (v + x \frac{d v}{d x})

乘开

(3 x + 5 vx) (v + x \frac{d v}{d x}) : 3 xv + 3 x^{2} \frac{d v}{d x} + 5 x v^{2} + 5 x^{2} v \frac{d v}{d x}

= x (3 xv + 3 x^{2} \frac{d v}{d x} + 5 x v^{2} + 5 x^{2} v \frac{d v}{d x})

乘开

x (3 xv + 3 x^{2} \frac{d v}{d x} + 5 x v^{2} + 5 x^{2} v \frac{d v}{d x}) : 3 x^{2} v + 3 x^{3} \frac{d v}{d x} + 5 x^{2} v^{2} + 5 x^{3} v \frac{d v}{d x}

= 3 x^{2} v + 3 x^{3} \frac{d v}{d x} + 5 x^{2} v^{2} + 5 x^{3} v \frac{d v}{d x}

e x p an d (5 e^{3} + 3 p^{2})^{6}

e x p an d e^{12 x} (6 x^{2} + 2 x)

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

e x p an d A (3, 3 0^{\circ}, 0) B (0, - 2, 5)

e x p an d - cos ((1 - n) π + 1)