Give algebraic proofs for even and odd functions that (a) even times even = even; odd...

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Give algebraic proofs for even and odd functions that (a) even times even = even; odd times odd = even; even times odd = odd. (b) The derivative of an even function is odd; the derivative of an odd function is even. Give algebraic proofs for even and odd functions that (a) even times even = even; odd times odd = even; even times odd = odd. (b) The derivative of an even function is odd; the derivative of an odd function is even.

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