Find the 27 derivative

Mathematics

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Finding the 27th derivative of this function by hand is an extremely complex and impractical task. The function is a rational function, and its higher-order derivatives do not follow a simple pattern that would allow for a concise general formula or simplification to zero.

Here's why it's so challenging:

  • The function y=(6x2+1)3(2x−5)4(x3−2x+1)−2y = (6x^2+1)^3 (2x-5)^4 (x^3-2x+1)^{-2} is a product of three functions. To find its nn-th derivative, one would typically use the generalized Leibniz rule for the derivative of a product:
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