y=2^x/lnx^2y'=[2^xln2*lnx^2-2^x*1/x^2*2x]/[lnx^2]^2
=2lnx(lnx)'=2lnx/x
y=(lnx)^xlny=xln(lnx)y'/y=ln(lnx)+x*(1/lnx)*(1/x)=ln(lnx)+1/lnxy'=(lnx)^x*ln(lnx)+(lnx)^(x-1)
等式左右同时取对数.lny=lnx*lnx^2 ,同时求导,y'/y=ln(2^x)/x+lnxln2,将y移到右边用X表示即可
y=(lnx)^x=e^{ln[(lnx)^x]}=e^[xln(lnx)]y'=e^[xln(lnx)]*[ln(lnx)+x*(1/lnx)*(1/x)]=[(lnx)^x] * [ln(lnx)+(1/lnx)]
若y1是一阶导数y1=(1-1/lnx)/lnx若y2是二阶导数y2=( 1-y1(2+lnx) )/xlnx
用导数是y=1/2x^2-lnx是吧它的导数是y=x-1/x通分x^2-1)/x因为lnx所以x>0所以令x^2-1=0所以阶级为(0,1)
y = (sinx)^lnxlny = (lnx) ln(sinx)(1/y) y' = (lnx) (1/sinx) cosx + (ln(sinx)) 1/x = (lnx) cotx + (1/x) lin(sinx)y' = [(lnx) cotx + (1/x) lin(sinx)]y = [(lnx) cotx + (1/x) lin(sinx)]((lnx) cotx + (1/x) lin(sinx))
已知:y=(2^x)lnx 有:y'=[(2^x)']lnx+(2^x)[lnx]'=(2^x)ln2lnx+(2^x)(1/x)
y'={lnx*(1/x)}'=1/(x^2)-lnx/(x^2)=(1-lnx)/(x^2)