Question

求导：y=log2(x) * log4(x)的导数

Answer 1

根据(lnx)'=1/x

而,log2(x)=lnx/(ln2)

就有:

y'=[log2(x)]'*log4(x)+log2(x)*[(log4(x)]'

=[1/(x*ln2)]*log4(x)+[1/(x*ln4)]*log2(x)

其实结果可以写为:

=[1/(x*ln2)]*lnx/(ln4)+[1/(x*ln4)]*lnx/(ln2)

=[(lnx)/x]*[1/(ln2*ln4)]