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

(X + Y) (X + Y^{^{'}})

(e^{x} - e^{- x})^{5}

\frac{( x ^{2} + 1 ) ^{3}}{6}

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

- \frac{5 x ( 4 x - 14 )}{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