A cool derivative
Calculus
Level
2
Which of the following answer choices shows the derivative of an odd function and an even function respectively?
even function and odd function
odd function and odd function
odd function and even function
even function and even function
none of the above
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Let f(x) be a given real valued function and E(x)=f(x)+f(-x) and O(x)=f(x)-f(-x).
Clearly E(x) and O(x) are respectively even and odd functions.
Now,E'(x)=f'(x)-f'(-x) which is an odd function and O'(x)=f'(x)-(-f'(-x))=f'(x)+f'(-x) which is an even function.