求导：y=log2(x) * log4(x)的导数y=log2(x) * log4(x)其中2,4为底数,求导数,2(Inr)/r(In2)(In4)是答案 请问为什么？

[loga(x)]'=(1/x)*loga(e) a为底 e为自然对数
log4(x)=(1/2)*log2(x)
y'=[log2(x)]'*log4(x)+log2(x)*[(log4(x)]'
=(1/x)*log2(e)*log4(x)+log2(x)*(1/x)*log4(e)
=(1/x)*log2(e)*(1/2)*log2(e)+log2(x)*(1/x)*(1/2)*log2(e)
=(1/2x)*log2(e)*log2(x)

Y'=1/(x.ln2).log4x+1/(x.ln4).log2x

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)]