Key to "What is the derivative of 1x?" - Plainmath

Simon Hanna

Answered question

2022-11-28

What is the derivative of

\frac{1}{x}

?

Answer & Explanation

Callum Richmond

Beginner2022-11-29Added 5 answers

Identify the derivative of

\frac{1}{x}

.
Let

\frac{1}{x} = x^{- 1} .

Next, determine the derivative of

x^{- 1}

that can be defined as follows:

\frac{d}{d x} (x^{- 1}) = - 1 x^{- 1 - 1} (∵ \frac{d}{d x} (x^{n}) = n x^{n - 1}) \Rightarrow = - 1 x^{- 2} \Rightarrow = - x^{- 2}

Hence, the derivative of

\frac{1}{x}

is

" - x^{- 2} "

.

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