1. Factorize the numerator:
x¹⁰ - 1 = (x - 1) (x⁹ + x⁸ + x⁷ + … + x² + x + 1)
Then

2. Recall that

Then

3. If f(x) = x² + 2x, then f'(x) = 2x + 2 and f''(x) = 2. This follows from the power rule for differentiation.
If you wish to show this using the definition, then






and





