What is the d/(dt)(2/3 t^{3/2}) ?

The d/(dt)(2/3 t^{3/2}) is t^{1/2}

What is the first d/(dt)(2/3 t^{3/2}) ?

The first d/(dt)(2/3 t^{3/2}) is t^{1/2}

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\frac{d}{d t} (\frac{2}{3} t^{\frac{3}{2}})

t^{\frac{1}{2}}

Solution steps

\frac{d}{d t} (\frac{2}{3} t^{\frac{3}{2}})

Take the constant out:

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

= \frac{2}{3} \frac{d}{d t} (t^{\frac{3}{2}})

Apply the Power Rule:

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

= \frac{2}{3} \cdot \frac{3}{2} t^{\frac{3}{2} - 1}

Simplify

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

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

What is the d/(dt)(2/3 t^{3/2}) ?
The d/(dt)(2/3 t^{3/2}) is t^{1/2}
What is the first d/(dt)(2/3 t^{3/2}) ?
The first d/(dt)(2/3 t^{3/2}) is t^{1/2}