求微分 y=e∧sin²x
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先求导:y‘=e^x-3cos3xx=1时,dy=y‘(1)dx=(e-3cos3)dx
dy=(2xsinx+x的平方cosx+2*e的2x次方)dx
dy=e^(x^x)(e^(xlnx))'dx=e^(x^x)*(x^x)*(1+lnx)
∫e^xsin(e^x+1)dx=∫sin(e^x+1)d(e^x+1)=-cos(e^x+1)+C验算:-cos(e^x+1)'=-[-sin(e^x+1)×e^x]=e^xsin(e^x+1)
y=xe^xdy=[x'e^x+x(e^x)']dx=(e^x+xe^x)dx
dy/dx==-(2e^x)/x^3+(e^x)/x^2我用数学软件算的,绝对不会错.
xy=e^(x+y)两边对x求导得:y+xy'=e^(x+y)(1+y')解得:y'=(e^(x+y)-y)/(x-e^(x+y))=(xy-y)/(x-xy)dy=[(xy-y)/(x-xy)]dx
dy=sinxdx²+x²dsinx=2sinxdx+x²cosxdx=(2sinx+x²cosx)dx再问:你微积分很厉害的?
y=sin(e∧x+1)dy=cos(e^x+1)d(e^x+1)=e^xcos(e^x+1)dx
1.d(cosx)^2=2cosx(-sinx)dx=-sin2xdx2.dsin(x²-1)=cos(x²-1)d(x²-1)=cos(x²-1)×2xdx=
dy=d(e^(1-3x))*cosx+(e^(1-3x))*d(cosx)=e^(1-3x)*(-3)*cosx*dx+e^(1-3x)*sinx*dx=e^(1-3x)*(sinx-3cosx)d
解微分方程吧y'=e^(x-y)dy/dx=e^x/e^ye^ydy=e^xdxe^y=e^x+cy=ln(e^x+c)再问:可以给具体点的步骤吗?拜托拜托1、y‘=e的x-y次幂2、y’+y=e的-
e^x-e^y=sin(xy)e^x-e^y*y'=cos(xy)*(y+xy')y'=(e^x-ycos(xy))/(e^y+xcos(xy))dy=(e^x-ycos(xy))/(e^y+xcos
分部积分法设u=x^ndv=(e^-x)*dx非常简单自己做
答:y=sin²x求导:y'=dy/dx=2sinxcosx=sin2x所以:微分dy=(sin2x)dx
e^x·dx+e^y·dy=2x·dxe^y·dy=(2x-e^x)·dxdy/dx=(2x-e^x)/e^y
y'=2e^2xcos(e^2x)把y看成复合函数sint,t=e^m,m=2x.复合函数求导,等于三个分别求导的积
y=sin(2x+1)dy=dsin(2x+1)=cos(2x+1)d(2x+1)=2cos(2x+1)dx