What is the derivative of-(13/(x^5)) ?

The derivative of-(13/(x^5)) is (65)/(x^6)

What is the first derivative of-(13/(x^5)) ?

The first derivative of-(13/(x^5)) is (65)/(x^6)

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\frac{d}{d x} (- \frac{13}{x ^{5}})

\frac{65}{x ^{6}}

Solution steps

\frac{d}{d x} (- \frac{13}{x ^{5}})

Take the constant out:

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

= - 13 \frac{d}{d x} (\frac{1}{x ^{5}})

Apply exponent rule:

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

= - 13 \frac{d}{d x} (x^{- 5})

Apply the Power Rule:

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

= - 13 (- 5 x^{- 5 - 1})

Simplify

- 13 (- 5 x^{- 5 - 1}) : \frac{65}{x ^{6}}

= \frac{65}{x ^{6}}

What is the derivative of-(13/(x^5)) ?
The derivative of-(13/(x^5)) is (65)/(x^6)
What is the first derivative of-(13/(x^5)) ?
The first derivative of-(13/(x^5)) is (65)/(x^6)