What is the d/(dt)((t)k(t-70)) ?

The d/(dt)((t)k(t-70)) is k(2t-70)

What is the first d/(dt)((t)k(t-70)) ?

The first d/(dt)((t)k(t-70)) is k(2t-70)

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\frac{d}{d t} ((t) k (t - 70))

k (2 t - 70)

Solution steps

\frac{d}{d t} ((t) k (t - 70))

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= k \frac{d}{d t} (t (t - 70))

Apply the Product Rule:

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

f = t, g = t - 70

= k (\frac{d t}{d t} (t - 70) + \frac{d}{d t} (t - 70) t)

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

\frac{d}{d t} (t - 70) = 1

= k (1 \cdot (t - 70) + 1 \cdot t)

Simplify

k (1 \cdot (t - 70) + 1 \cdot t) : k (2 t - 70)

= k (2 t - 70)

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