calculate the vector that contains the values of the first derivative using central difference in javascript

The central difference formula gives us an estimate of the first derivative of a function at a point. Using this formula and an array of function values, we can calculate a new array containing the values of the first derivative.

Here's how to do it in JavaScript:

index.tsx
function centralDifference(values) {
  const n = values.length
  const result = []

  for (let i = 0; i < n; i++) {
    if (i === 0) {
      // Use forward difference formula for first element
      result.push((values[1] - values[0]))
    } else if (i === n - 1) {
      // Use backward difference formula for last element
      result.push((values[n-1] - values[n-2]))
    } else {
      // Use central difference formula for all other elements
      result.push((values[i+1] - values[i-1])/2)
    }
  }

  return result
}
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The values parameter is an array containing the function values at each point. The function returns a new array containing the values of the first derivative estimated using the central difference formula.

The code checks for edge cases where the first or last element of the array is being processed, and uses forward or backward difference formulas respectively. For all other elements, it uses the central difference formula.

You can call this function like this:

index.tsx
const values = [1, 2, 4, 7, 11]
const firstDerivative = centralDifference(values)
console.log(firstDerivative)
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This will output an array containing the values of the first derivative estimated using the central difference formula.