If (f(x+y)=f(x)f(y) ) for all (x,y R ) and (f(5)=2 ), (f'(0)=3 )

MATHEMATICS · Subjective · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

If f(x+y)=f(x)f(y)f(x+y)=f(x)f(y) for all x,y∈Rx,y\in\mathbb{R} and f(5)=2f(5)=2, f′(0)=3f'(0)=3, then using the definition of derivatives, find f′(5)f'(5).

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