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

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

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Q. What is the value of ddx(1x) \frac{d}{d x}\left(\frac{1}{x}\right) at x=6 x=6 ?
  1. Identify Function: Identify the function to differentiate.\newlineWe are given the function f(x)=1xf(x) = \frac{1}{x}.
  2. Differentiate Function: Differentiate the function with respect to xx. The derivative of f(x)=1xf(x) = \frac{1}{x} with respect to xx is f′(x)=−1x2f'(x) = -\frac{1}{x^2}.
  3. Substitute x=6x=6: Substitute x=6x=6 into the derivative to find its value at that point.f′(6)=−1(62)=−136.f'(6) = -\frac{1}{(6^2)} = -\frac{1}{36}.
  4. Check for Errors: Check for any mathematical errors in the differentiation and substitution process.\newlineNo errors were made in the differentiation or substitution.

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