Question

Providing f′(1)=1 and f satisfying f(xy)=xf(y)+yf(x) then find f(x)

Answer 1

f'(1×1)=1

=1×f(1)+1×f(1)

so,f(x) =1

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Answer 2

Answer:

f'(1) = 1

f'(1.1).= 1

f(x.y) = x.f(y) + y.f(x)

f(x) = 1