What is the d/(dt)(2sqrt(t)) ?

The d/(dt)(2sqrt(t)) is 1/(sqrt(t))

What is the first d/(dt)(2sqrt(t)) ?

The first d/(dt)(2sqrt(t)) is 1/(sqrt(t))

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

\frac{1}{t}

Solution steps

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

Take the constant out:

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

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

Apply radical rule:

a = a^{\frac{1}{2}}

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= 2 \cdot \frac{1}{2} t^{\frac{1}{2} - 1}

Simplify

2 \cdot \frac{1}{2} t^{\frac{1}{2} - 1} : \frac{1}{t}

= \frac{1}{t}

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