For the function f(x) = x¹⁰⁰/100 + x⁹⁹/99 + ... + x²/2 + x + 1. Prove that f′(1) = 100 f′(0).

Question

TextDerivative of Polynomial Functions

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Compute the derivative of 6x¹⁰⁰ – x⁵⁵ + x.

Find the derivative of f(x) = 1 + x + x² + x³ +... + x⁵⁰ at x = 1.

Find the derivative of xⁿ + axⁿ⁻¹ + a²xⁿ⁻² + . . . + aⁿ⁻¹x + aⁿ for some fixed real number a.

TextDerivative of Polynomial Functions

(x + a)

4√x - 2

(ax + b)ⁿ