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?
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![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?](/uploads/image/z/581194-10-4.jpg?t=%E6%B1%82%E5%AF%BC%EF%BC%9Ay%3Dlog2%28x%29+%2A+log4%28x%29%E7%9A%84%E5%AF%BC%E6%95%B0y%3Dlog2%28x%29+%2A+log4%28x%29%E5%85%B6%E4%B8%AD2%2C4%E4%B8%BA%E5%BA%95%E6%95%B0%2C%E6%B1%82%E5%AF%BC%E6%95%B0%2C2%28Inr%29%2Fr%28In2%29%28In4%29%E6%98%AF%E7%AD%94%E6%A1%88+%E8%AF%B7%E9%97%AE%E4%B8%BA%E4%BB%80%E4%B9%88%EF%BC%9F)
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?
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?
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?
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)]
Y'=1/(x.ln2).log4x+1/(x.ln4).log2x
[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)