JEE Main2013MathematicsDifferentiationActual

If f(x)= ( x) and f^ (x)+ x f^ (x)+g(x)=0 , then g(x) is :

Options

A^2 x ( x)
B^2 x ( x)
C^2 x ( x)
D^2 x ( x)

Correct answer

D. ^2 x ( x)

Step-by-step solution

aligned & f(x)= ( x) & f^ (x)= ( x) x & f^ (x)=- ( x) ^2 x+ ( x) . & (- x) & =- ^2 x ( x)- x ( x) & Now f^ (x)+ x . f^ (x)+g(x)=0 & g(x)= ^2 x ( x)+ x ( x) & - x x ( x) & g(x)= ^2 x ( x) . & aligned

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