What is the d/(dt)(\sqrt[5]{t}) ?

The d/(dt)(\sqrt[5]{t}) is 1/(5t^{4/5)}

What is the first d/(dt)(\sqrt[5]{t}) ?

The first d/(dt)(\sqrt[5]{t}) is 1/(5t^{4/5)}

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\frac{1}{5 t ^{\frac{4}{5}}}

Solution steps

Apply radical rule:

= \frac{d}{d t} (t^{\frac{1}{5}})

Apply the Power Rule:

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

= \frac{1}{5} t^{\frac{1}{5} - 1}

Simplify

\frac{1}{5} t^{\frac{1}{5} - 1} : \frac{1}{5 t ^{\frac{4}{5}}}

= \frac{1}{5 t ^{\frac{4}{5}}}

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What is the d/(dt)(\sqrt[5]{t}) ?
The d/(dt)(\sqrt[5]{t}) is 1/(5t^{4/5)}
What is the first d/(dt)(\sqrt[5]{t}) ?
The first d/(dt)(\sqrt[5]{t}) is 1/(5t^{4/5)}