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

The first d/(dt)((x)(2x-1)) is 4t-1

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d/(dt)((x)(2x-1))

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

4 t - 1

Solution steps

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

Apply the Product Rule:

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

f = t, g = 2 t - 1

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

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

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

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

Simplify

= 4 t - 1

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