What is the derivative of a/(x^b) ?

The derivative of a/(x^b) is -abx^{-b-1}

What is the first derivative of a/(x^b) ?

The first derivative of a/(x^b) is -abx^{-b-1}

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\frac{d}{d x} (\frac{a}{x ^{b}})

- ab x^{- b - 1}

Solution steps

\frac{d}{d x} (\frac{a}{x ^{b}})

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

= a (- b x^{- b - 1})

Simplify

= - ab x^{- b - 1}

What is the derivative of a/(x^b) ?
The derivative of a/(x^b) is -abx^{-b-1}
What is the first derivative of a/(x^b) ?
The first derivative of a/(x^b) is -abx^{-b-1}