IIT JEE 1983 Maths - True or False Q7
Calculus
Level
2
True or False?
The derivative of an even function is always an odd function.
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False
True
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1 solution
Say f(x)=n . Hence f(-x)= n as it is even.
Now when differentiate we get F'(x) =dn/dx an -f'(-x)=dn/dx......
Adding both we get f'(x)+f'(-x)=0 which proves that f'(x) is odd