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If f(x)=(g(x)+g(-x))/2 + 2/[h(x)+h(-x)]^...

If `f(x)=(g(x)+g(-x))/2 + 2/[h(x)+h(-x)]^(-1),` where `g` and `h` are differentiable functions, then `f' (0)`

A

1

B

`(1)/(2)`

C

`(3)/(2)`

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
Given , ` f(x) = (g(x) + g(-x))/(2) + (2)/([h (x) + h(-x)]^(1))`
` rArr f(x) = (g'(x)- g'(-x))/(2) + 2 [h(x) + h(-x)]`
On differnetiating both sides w.r.t.x, we get
`f'(x)= (g'(x) - g'(-x))/(2)+ 2[h'(x) - h'(-x)]`
`therefore f'(0)= (g'(0) - g'(0))/(2)+ 2[h'(0) - h'(0)]= 0` .
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