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Viluxent Set 1 Paper 1 · Q8

Paper 1Functions & graphs

A differentiable function ff is defined for all x>0x>0 and satisfies

f(xy)=f(x)+f(y)for all x,y>0,f(xy)=f(x)+f(y)\qquad\text{for all }x,y>0,

together with f(2)=1f(2)=1. Find f′(8)f'(8).

A18\frac18
Bln⁡28\frac{\ln2}{8}
C18ln⁡2\frac1{8\ln2}
D38ln⁡2\frac3{8\ln2}
E18ln⁡8\frac1{8\ln8}
F12ln⁡2\frac1{2\ln2}

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