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Let f(x) be an even function. Then  \mathrm{f^{\prime}(x)} 

Option: 1

is an even function
 


Option: 2

is an odd function


Option: 3

may be even or odd
 


Option: 4

none of these.


Answers (1)

best_answer

Since f(x) is an even function, therefore
\mathrm{f(-x)=f(x) \text { for all } x }
\mathrm{\Rightarrow -f^{\prime}(-x)=f^{\prime}(x) \text { for all } x \\ }

\mathrm{\Rightarrow f^{\prime}(-x)=-f^{\prime}(x) \text { for all } x \\ }
\mathrm{\Rightarrow f^{\prime}(x) \text { is an odd function. } }\mathrm{\Rightarrow f^{\prime}(x) \text { is an odd function. } }
 

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Pankaj

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