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

The derivative of (x^{n-1}/n) is (x^{n-2}(n-1))/n

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

The first derivative of (x^{n-1}/n) is (x^{n-2}(n-1))/n

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

\frac{x ^{n - 2} ( n - 1 )}{n}

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

\frac{1}{n} (n - 1) x^{n - 1 - 1} : \frac{x ^{n - 2} ( n - 1 )}{n}

= \frac{x ^{n - 2} ( n - 1 )}{n}

What is the derivative of (x^{n-1}/n) ?
The derivative of (x^{n-1}/n) is (x^{n-2}(n-1))/n
What is the first derivative of (x^{n-1}/n) ?
The first derivative of (x^{n-1}/n) is (x^{n-2}(n-1))/n