What is the d/(dt)(6sqrt(t)) ?

The d/(dt)(6sqrt(t)) is 3/(sqrt(t))

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

The first d/(dt)(6sqrt(t)) is 3/(sqrt(t))

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

\frac{3}{t}

Solution steps

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

Take the constant out:

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

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

Apply radical rule:

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

= 6 \frac{d}{d t} (t^{\frac{1}{2}})

Apply the Power Rule:

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

= 6 \cdot \frac{1}{2} t^{\frac{1}{2} - 1}

Simplify

6 \cdot \frac{1}{2} t^{\frac{1}{2} - 1} : \frac{3}{t}

= \frac{3}{t}

v^{\frac{3}{2}} (v + c e^{v})

\frac{d}{d x} (\frac{5 x - 2}{4 x + 3})

f (x) = arcsec (e^{2 x})

y^{^{'}} + \frac{1}{2} y = 5

x \to 7 - lim (x - 7)