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

The derivative of (-5/(x^5)) is (25)/(x^6)

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

The first derivative of (-5/(x^5)) is (25)/(x^6)

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

\frac{25}{x ^{6}}

Solution steps

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

Simplify

\frac{- 5}{x ^{5}} : - \frac{5}{x ^{5}}

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

- 5 (- 5 x^{- 5 - 1}) : \frac{25}{x ^{6}}

= \frac{25}{x ^{6}}

\int \frac{x ^{2}}{csc ( x )} d x

\int_{0}^{5} \frac{1}{x ^{\frac{19}{20}}} d x

\int_{0}^{4} (6 - x^{2}) d x

x \to \infty lim (0. 1^{x})

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

What is the derivative of (-5/(x^5)) ?
The derivative of (-5/(x^5)) is (25)/(x^6)
What is the first derivative of (-5/(x^5)) ?
The first derivative of (-5/(x^5)) is (25)/(x^6)