What is expand (2t^3-2t^2+t-1)(dx)/(dt) ?

The solution to expand (2t^3-2t^2+t-1)(dx)/(dt) is 2t^3(dx)/(dt)-2t^2(dx)/(dt)+t(dx)/(dt)-(dx)/(dt)

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expand (2t^3-2t^2+t-1)(dx)/(dt)

expand

(2 t^{3} - 2 t^{2} + t - 1) \frac{d x}{d t}

2 t^{3} \frac{d x}{d t} - 2 t^{2} \frac{d x}{d t} + t \frac{d x}{d t} - \frac{d x}{d t}

Solution steps

(2 t^{3} - 2 t^{2} + t - 1) \frac{d x}{d t}

Distribute parentheses

= \frac{d x}{d t} 2 t^{3} + \frac{d x}{d t} (- 2 t^{2}) + \frac{d x}{d t} t + \frac{d x}{d t} (- 1)

Apply minus-plus rules

+ (- a) = - a

= 2 t^{3} \frac{d x}{d t} - 2 t^{2} \frac{d x}{d t} + t \frac{d x}{d t} - 1 \frac{d x}{d t}

Multiply:

1 \frac{d x}{d t} = \frac{d x}{d t}

= 2 t^{3} \frac{d x}{d t} - 2 t^{2} \frac{d x}{d t} + t \frac{d x}{d t} - \frac{d x}{d t}

tan (\frac{β}{2}) \cdot (1 + cos (β))

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

x + (y - 2 x) y^{'} (x)

e^{θ} (- θt + \frac{t ^{2}}{2})

What is expand (2t^3-2t^2+t-1)(dx)/(dt) ?
The solution to expand (2t^3-2t^2+t-1)(dx)/(dt) is 2t^3(dx)/(dt)-2t^2(dx)/(dt)+t(dx)/(dt)-(dx)/(dt)