What is the derivative of 1/(x^{19)} ?

The derivative of 1/(x^{19)} is -(19)/(x^{20)}

What is the first derivative of 1/(x^{19)} ?

The first derivative of 1/(x^{19)} is -(19)/(x^{20)}

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derivative of

\frac{1}{x ^{19}}

- \frac{19}{x ^{20}}

Solution steps

\frac{d}{d x} (\frac{1}{x ^{19}})

Apply exponent rule:

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

= \frac{d}{d x} (x^{- 19})

Apply the Power Rule:

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

= - 19 x^{- 19 - 1}

Simplify

- 19 x^{- 19 - 1} : - \frac{19}{x ^{20}}

= - \frac{19}{x ^{20}}

What is the derivative of 1/(x^{19)} ?
The derivative of 1/(x^{19)} is -(19)/(x^{20)}
What is the first derivative of 1/(x^{19)} ?
The first derivative of 1/(x^{19)} is -(19)/(x^{20)}