What is the derivative of (10/(x^9)) ?

The derivative of (10/(x^9)) is -(90)/(x^{10)}

What is the first derivative of (10/(x^9)) ?

The first derivative of (10/(x^9)) is -(90)/(x^{10)}

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\frac{d}{d x} (\frac{10}{x ^{9}})

- \frac{90}{x ^{10}}

Solution steps

\frac{d}{d x} (\frac{10}{x ^{9}})

Take the constant out:

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

= 10 \frac{d}{d x} (\frac{1}{x ^{9}})

Apply exponent rule:

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

= 10 \frac{d}{d x} (x^{- 9})

Apply the Power Rule:

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

= 10 (- 9 x^{- 9 - 1})

Simplify

10 (- 9 x^{- 9 - 1}) : - \frac{90}{x ^{10}}

= - \frac{90}{x ^{10}}

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What is the derivative of (10/(x^9)) ?
The derivative of (10/(x^9)) is -(90)/(x^{10)}
What is the first derivative of (10/(x^9)) ?
The first derivative of (10/(x^9)) is -(90)/(x^{10)}