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What is the value of
(d)/(dx)((1)/(x)) at
x=6 ?

What is the value of $\frac{d}{d x}\left(\frac{1}{x}\right)$ at $x=6$ ?

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Find values of derivatives using limits

Full solution

Q. What is the value of

\frac{d}{d x}\left(\frac{1}{x}\right)

at

x=6

?

Identify Function: Identify the function to differentiate. $\newline$ We are given the function $f(x) = \frac{1}{x}$ .
Differentiate Function: Differentiate the function with respect to $x$ . The derivative of $f(x) = \frac{1}{x}$ with respect to $x$ is $f'(x) = -\frac{1}{x^2}$ .
Substitute $x=6$ : Substitute $x=6$ into the derivative to find its value at that point. $f'(6) = -\frac{1}{(6^2)} = -\frac{1}{36}.$
Check for Errors: Check for any mathematical errors in the differentiation and substitution process. $\newline$ No errors were made in the differentiation or substitution.

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