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

The derivative of In\sqrt[5]{x} is (nI)/(5x^{4/5)}

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

The first derivative of In\sqrt[5]{x} is (nI)/(5x^{4/5)}

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\frac{n I}{5 x ^{\frac{4}{5}}}

Solution steps

Treat

n, I

as a constant

Take the constant out:

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

Apply radical rule:

= I n \frac{d}{d x} (x^{\frac{1}{5}})

Apply the Power Rule:

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

= I n \frac{1}{5} x^{\frac{1}{5} - 1}

Simplify

I n \frac{1}{5} x^{\frac{1}{5} - 1} : \frac{n I}{5 x ^{\frac{4}{5}}}

= \frac{n I}{5 x ^{\frac{4}{5}}}

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