What is the first d/(dt)(6sin(t)) ?

The first d/(dt)(6sin(t)) is 6cos(t)

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d/(dt)(6sin(t))

\frac{d}{d t} (6 sin (t))

6 cos (t)

Solution steps

\frac{d}{d t} (6 sin (t))

Take the constant out:

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

= 6 \frac{d}{d t} (sin (t))

Apply the common derivative:

\frac{d}{d t} (sin (t)) = cos (t)

= 6 cos (t)

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