What is expand x(3x+5vx)(v+x(dv)/(dx)) ?

The solution to expand x(3x+5vx)(v+x(dv)/(dx)) is 3x^2v+3x^3(dv)/(dx)+5x^2v^2+5x^3v(dv)/(dx)

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expand x(3x+5vx)(v+x(dv)/(dx))

expand

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}

Solution steps

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

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

Expand

(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})

Expand

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}

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

e^{12 x} (6 x^{2} + 2 x)

\frac{1}{x ( x ^{2} + 2 )}

A (3, 3 0^{\circ}, 0) B (0, - 2, 5)

tan (π (x - \frac{1}{2}))

What is expand x(3x+5vx)(v+x(dv)/(dx)) ?
The solution to expand x(3x+5vx)(v+x(dv)/(dx)) is 3x^2v+3x^3(dv)/(dx)+5x^2v^2+5x^3v(dv)/(dx)