∵f(x+y)=f(x)⋅f′(y)+f′(x)⋅f(y),∀x,y∈R....(i) Andf(0)=1....(ii) Now replacexby zero andyby zero we get ‌f(0)=f(0)f′(0)+f′(0)f(0) ‌1=f′(0)+f′(0) ‌∴‌‌f′(0)=‌
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....(iii) Now replace y by zero in equation (i), we get f(x)=‌