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

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

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

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

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

x^{n}

Solution steps

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

Take the constant out:

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

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

Simplify

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

= x^{n}

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\int (x - 6)^{2} d x

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