y＝ln根号下x,求dy-搜答案-智慧作业帮

1/(x+根号下a方加x方)乘以x+根号下a方加x方的导数乘以1+1/2a方加x方导数x+根号下a方加x方的导数=1+1/2a方加x方1+1/2a方加x方导数=自己算一步一步脱

1/2*ln(x^2+y^2)=arctany/x两边对x求导,得1/2*1/(x^2+y^2)*(2x+2y*y')=1/[1+(y/x)^2]*(y'*x-y)/x^2化简得y'=(x+y)/(x

y'=(1/x*x²-2xlnx)/x的4次方=(x-2xlnx)/x的4次方所以dy=(x-2xlnx)/x的4次方dx

∵y＝ln［x＋√（x^2＋a^2）］,∴e^y＝x＋√（x^2＋a^2）,∴（e^y－x）^2＝x^2＋a^2,∴2（e^y－x）（e^y－x）′＝2x,∴［x＋√（x^2＋a^2）－x］［（e^y

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x/y=ln(y/x)x(-1/y^2)y'+1/y=x/y(-y/x^2+y'/x)(1/y+x/y^2)y'=1/y+1/x[(y+x)/y^2]y'=(x+y)/xyy'=y/x

y=ln(x+x^2) 求dy

y'=1/(x+x^2)*(2x+1)=(2x+1)/(x+x^2)dy=(2x+1)/(x+x^2)dx

y＝ln(2x＋1)求dy

2/2x+1

dy=y'dx=(x/(1+x^2)-e^(-x))dx

因为所以

dy/dx=sin(x^1/2)/y*x^(1/2)1/ydy=sin(x^1/2)/x^(1/2)dx=2d(sin(x^1/2))lny=2sin(x^1/2)+cy=c1*e^(2sin(x^1

dy=x*根号（1+x^2）分之一*dx

y=xe^(Cx+1),C为任意常数详细过程点下图查看

y=ln(ln平方x),求dy

y=2ln(lnx)dy=y'dx=(2/lnx)*(1/x)dx=2/xlnxdx

...y＝ln（x＋e^x^2）dy=（x＋e^x^2）^(-1)*(1+2xe^x^2)x^y就是x的y次方

y＝ln（ln²x）求dy

ln²x=u,dy=dlnu=u'/u=2lnx*1/xdx/u=2/xlnxdx

两边对【x】求导,注意,y是x的函数,利用复合函数求导1/[1+(y/x)^2]×(y/x)'=1/2×1/(x^2+y^2)×(x^2+y^2)',也就是：x^2/(x^2+y^2)×(xy'-y)

y=ln(1+e)+ln(1+x)+ln(sinx)dy=(cosx/sinx)+1/(1+x)