derivative of a periodic function is again same period function cucet 2017 real analysis mathematics

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Real Analysis: Interior points, limit points, open sets, closed sets, bounded sets, connected sets, compact sets, completeness of R. Power series (of real variable), Taylor's series, radius and interval of convergence, term-wise differentiation and integration of power series.
Sequences and Series of Real Numbers: Sequence of real numbers, convergence of sequences, bounded and monotone sequences, convergence criteria for sequences of real numbers, Cauchy sequences, subsequences, Bolzano-Weierstrass theorem. Series of real numbers, absolute convergence, tests of convergence for series of positive terms — comparison test, ratio test, root test; Leibniz test for convergence of alternating series.
Results on Periodic functions
1. If f(x) has fundamental period T,then f(ax) has period T/|a| .
2. Linear combination of periodic functions may not be periodic.
For example:f(x)=cos⁡x,g(x)=cos⁡πx
f(x) is periodic function with period 2π and g(x) is periodic function with period 2 but f(x)+g(x) is not
periodic function.
3. Composition of two non-periodic functions can be periodic.
4. Composition of two periodic functions can be non-periodic.
5. Non constant algebraic function can never be periodic.

derivative of a periodic function is again same period function cucet 2017 real analysis mathematics
tag 22082021
CUCET 2017, 45