What is the derivative of (x^n/n) ?

The derivative of (x^n/n) is x^{n-1}

What is the first derivative of (x^n/n) ?

The first derivative of (x^n/n) is x^{n-1}

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\frac{d}{d x} (\frac{x ^{n}}{n})

x^{n - 1}

Solution steps

\frac{d}{d x} (\frac{x ^{n}}{n})

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

\frac{1}{n} n x^{n - 1} : x^{n - 1}

= x^{n - 1}

What is the derivative of (x^n/n) ?
The derivative of (x^n/n) is x^{n-1}
What is the first derivative of (x^n/n) ?
The first derivative of (x^n/n) is x^{n-1}