What is the d/(dt)((X)((X-1)(1-2X))) ?

The d/(dt)((X)((X-1)(1-2X))) is -6t^2+6t-1

What is the first d/(dt)((X)((X-1)(1-2X))) ?

The first d/(dt)((X)((X-1)(1-2X))) is -6t^2+6t-1

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\frac{d}{d t} ((t) ((t - 1) (1 - 2 t)))

- 6 t^{2} + 6 t - 1

Solution steps

\frac{d}{d t} ((t) ((t - 1) (1 - 2 t)))

Apply the Product Rule:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = t, g = (t - 1) (1 - 2 t)

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

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

\frac{d}{d t} ((t - 1) (1 - 2 t)) = - 4 t + 3

= 1 \cdot (t - 1) (1 - 2 t) + (- 4 t + 3) t

Simplify

1 \cdot (t - 1) (1 - 2 t) + (- 4 t + 3) t : - 6 t^{2} + 6 t - 1

= - 6 t^{2} + 6 t - 1

d x (x^{2} + y^{2})

(2 π - x) cot (x)

π (12 - h)^{2} h

8 x^{2} + 11 x^{2}

9 (x + d x)^{3}

What is the d/(dt)((X)((X-1)(1-2X))) ?
The d/(dt)((X)((X-1)(1-2X))) is -6t^2+6t-1
What is the first d/(dt)((X)((X-1)(1-2X))) ?
The first d/(dt)((X)((X-1)(1-2X))) is -6t^2+6t-1