Question

用dy/dx的形式求导数y=a^x

Answer 1

y' = lim(t->0)(a^(x+t)-a^x)/t
= a^x * lim(t->0)(a^t-1)/t
= a^x * lna * lim(t->0)(e^(t*lna)-1)/t*lna
根据等价无穷小,后面的lim等于1
所以y'=a^x * lna