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For a differntiable function , define D^...

For a differntiable function , define `D^(**)f(x) = L t_(h to 0) (f^2(x + h) - f^2(x))/(h)` where `f'(x) = (f(x))^2` for example, `D^(**)f(x) = 2x` if `f(x) = x, D^(**)f(x) = 2 sin x cos x ` if `f(x) = sin xD^(**)f(x) = 2e^(2x)` if `f(x) = e^(x)`
If `f(x) = tan x` and `g(x) = log x ` the `D^(**)(fg) (1)` =

A

`tan 1`

B

`(tan 1)^2`

C

`0`

D

`2(tan 1)^2`

Text Solution

Verified by Experts

The correct Answer is:
C
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