What is the derivative of 5/(x^9) ?

The derivative of 5/(x^9) is -(45)/(x^{10)}

What is the first derivative of 5/(x^9) ?

The first derivative of 5/(x^9) is -(45)/(x^{10)}

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\frac{d}{d x} (\frac{5}{x ^{9}})

- \frac{45}{x ^{10}}

Solution steps

\frac{d}{d x} (\frac{5}{x ^{9}})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{1}{x ^{9}})

Apply exponent rule:

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

= 5 \frac{d}{d x} (x^{- 9})

Apply the Power Rule:

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

= 5 (- 9 x^{- 9 - 1})

Simplify

5 (- 9 x^{- 9 - 1}) : - \frac{45}{x ^{10}}

= - \frac{45}{x ^{10}}

What is the derivative of 5/(x^9) ?
The derivative of 5/(x^9) is -(45)/(x^{10)}
What is the first derivative of 5/(x^9) ?
The first derivative of 5/(x^9) is -(45)/(x^{10)}