What is the derivative of 3/(x^{13)} ?

The derivative of 3/(x^{13)} is -(39)/(x^{14)}

What is the first derivative of 3/(x^{13)} ?

The first derivative of 3/(x^{13)} is -(39)/(x^{14)}

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derivative of

\frac{3}{x ^{13}}

- \frac{39}{x ^{14}}

Solution steps

\frac{d}{d x} (\frac{3}{x ^{13}})

Take the constant out:

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

= 3 \frac{d}{d x} (\frac{1}{x ^{13}})

Apply exponent rule:

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

= 3 \frac{d}{d x} (x^{- 13})

Apply the Power Rule:

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

= 3 (- 13 x^{- 13 - 1})

Simplify

3 (- 13 x^{- 13 - 1}) : - \frac{39}{x ^{14}}

= - \frac{39}{x ^{14}}

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What is the derivative of 3/(x^{13)} ?
The derivative of 3/(x^{13)} is -(39)/(x^{14)}
What is the first derivative of 3/(x^{13)} ?
The first derivative of 3/(x^{13)} is -(39)/(x^{14)}