y=f(x), where f satisfies the relation `f(x+y)=2f(x)+xf(y)+ysqrt(f(x))`,`AAx,y epsilon R` and f'(0)=0.Then f(6)is equal ______

Explanation

`f'(x)=underset(hrarr0)lim(f(x+h)-f(x+0))/(h)`
`"or "underset(hrarr0)lim(2f(x)+xf(h)+hsqrt(f(x))-2f(x)-xf(0)-0sqrt(f(x)))/(h)`
as f(0)=0
`"or "underset(hrarr0)lim((f(h)-f(0))/(h-0))+sqrt(f(x))=f'(0)+sqrt(f(x))`
`"or "f'(x)=sqrt(f(x))" "[becausef'(0)=0]`
`"or "int(f'(x))/(sqrt(f(x)))dx=intdx`
`"or "2sqrt(f(x))=x+c`
`"or "f(x)=(x^(2))/(4)" "[becausef(0)=0]`