Question

设f(x)在x=0处可导，且limx→0{[f(x）—f(kx)]/x } =L(其中k,L为常数，且L不等于1），求f'(x).

要详细的过程。

Answer 1

limx→0{[f(x）—f(kx)]/x }
=limx→0{[f‘(x）—kf’(kx)] }
=f'(0)-kf'(0)=L
(1-k)f'(0)=L
k≠1时
f'(0)=L/(1-k)