If f(x) is a differentiable function fo...

If f(x) is a differentiable function for all `x gt 0` and `lim_(y to x)(y^(2)f(x)-x^(2)f(y))/(y-x)=2`, then the value of f'(x) is -

A

`(1)/(x^(2)) [x f(x)-1]`

B

`(2)/(x^(2))[f(x)-2]`

C

`(1)/(x^(2))[x f(x)-2]`

D

`(2)/(x^(2))[x f(x) -1]`

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The correct Answer is:

D

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