MediumDerivatives

Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) §2.1 The Derivative of a Function, #18 · Calculus · Derivatives

For … the centered difference … is

For $f (x) = 1/ x$ the centered difference $f (x + h) - f (x - h)$ is $1/ (x + h) - 1/ (x - h)$ . Subtract by using the common denominator $(x + h) (x - h)$ . Then divide by $2 h$ and set $h = 0$ . Why divide by $2 h$ to obtain the correct derivative?

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Gilbert Strang, Calculus, 3rd edition (Wellesley-Cambridge Press; MIT OpenCourseWare RES.18-001) · §2.1 The Derivative of a Function, #18

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