Question

Differentiation Sum
Plss Proper Explanation..​

Answer 1

Answer:

1

We will prove that, the derivative of an odd function is even Suppose f is an odd function Therefore f(-x) = - f(x) , for every x in R

Taking Derivatives of both the sides with respect to x , we get d/dx f(-x) = d/dx [-f(x)]

Using chain Rule , we get, f'(-x).d/dx (-x) = - f'(x)

i.e f'(-x) .(-1) = - f'(x) Therefore - f'(-x) = - f'(x) , cancelling -ve signs from both the sides, we get f'(-x) = f'(x) , for all x in R This proves that, f is an even function.

Similarly we can prove that, the derivative of an even function is odd

Answer 2

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here is your answer