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put x=y =0
f(0) = f(0) + f(0)
=>f(0) = 0
f'(x)= lim(y->0)[f(x+y) - f(x)]/y
= lim(y->0)[e^xf(y)+e^yf(x) - f(x)]/y
= e^x lim(y->0)[f(0+y)-f(0)]/y + f(x) lim(y->0)( e^y - 1)/y
= e^xf'(0) + f(x)
= e^(x+1) + f(x)
f(0) = f(0) + f(0)
=>f(0) = 0
f'(x)= lim(y->0)[f(x+y) - f(x)]/y
= lim(y->0)[e^xf(y)+e^yf(x) - f(x)]/y
= e^x lim(y->0)[f(0+y)-f(0)]/y + f(x) lim(y->0)( e^y - 1)/y
= e^xf'(0) + f(x)
= e^(x+1) + f(x)
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