What is the derivative of \sqrt[5]{t} ?

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

What is the first derivative of \sqrt[5]{t} ?

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

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derivative of

5 t

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

Solution steps

\frac{d}{d t} (5 t)

Apply radical rule:

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

= \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}}}

\int \frac{∣ x ∣}{x} d x

\int \frac{x arctan ( x )}{1 + x ^{2}} d x

cos^{2} (14 t)

\frac{s - 1}{s ( s + 4 ) + 3}

y^{^{''}} + 2 y = 0

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