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Let the derivative of f(x) be defined as...

Let the derivative of `f(x)` be defined as `D^(**)f(x)=lim_(hto0)(f^(2)x+h-f^(2)(x))/(h),` where `f^(2)(x)={f(x)}^(2)`.
If `u=f(x),v=g(x)`, then the value of `D^(**)((u)/(v))` is.

A

`(u^(2)(D^(**)v)-v^(2)(D^(**)u))/(v^(4))`

B

`(u(D^(**)v)-v(D^(**)u))/(v^(2))`

C

`(v^(2)(D^(**)u)-u^(2)(D^(**)v))/(v^(4))`

D

`(v(D^(**)u)-u(D^(**)v))/(v^(2))`

Text Solution

Verified by Experts

The correct Answer is:
C
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