What is the first d/(dt)(2t(n/4)+c) ?

The first d/(dt)(2t(n/4)+c) is n/2

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d/(dt)(2t(n/4)+c)

\frac{d}{d t} (2 t (\frac{n}{4}) + c)

\frac{n}{2}

Solution steps

\frac{d}{d t} (2 t (\frac{n}{4}) + c)

Simplify

2 t (\frac{n}{4}) + c : \frac{n t}{2} + c

= \frac{d}{d t} (\frac{n t}{2} + c)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d t} (\frac{n t}{2}) + \frac{d c}{d t}

\frac{d}{d t} (\frac{n t}{2}) = \frac{n}{2}

\frac{d c}{d t} = 0

= \frac{n}{2} + 0

Simplify

= \frac{n}{2}