SOLUTION: Using the chain rule, show that the following statements are always true: a) If f(x) is an odd function then f'(x) is an even function b) If f(x) is an even function then f'

Question 1200824: Using the chain rule, show that the following statements are always true:
a) If f(x) is an odd function then f'(x) is an even function
b) If f(x) is an even function then f'(x) is an odd function
Answer by Edwin McCravy(20055) (Show Source): You can put this solution on YOUR website!

g(x) is an even function if and only if g(-x) = g(x)
g(x) is an odd function if and only if g(-x) = -g(x)

a) If f(x) is an odd function then f'(x) is an even function




Take derivatives of both sides:





Divide both sides by -1



So f'(x) is an even function.

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b) If f(x) is an even function then f'(x) is an odd function




Take derivatives of both sides:





Divide both sides by -1



So f'(x) is an odd function.

Edwin

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