ey的x次方=πx的y次方确定y是x的函数-搜答案-百度作业网

由x^(x+y)=y^12得x+y=logx(y^12)……………①由y^(x+y)=x^3得x+y=logy(x^3)……………②所以logx(y^12)=logy(x^3)即12logx(y)=3

这种一般要对数法两边取对数：ylnx=xlny再对x求导,把y看成复合函数：y'lnx+y/x=lny+xy'/y得：y'=(lny-y/x)/(lnx-x/y)再问：我们老师讲的分别对x和y求导，死

Y=sinx的X次方求导

详细解答请见图片,点击放大,再点击再放大.

x+9y=y-3x4x=-8yx=-2y则x²=4y²所以原式=(4y²-y²)/(4y²+y²)=3y²/5y²=3/

xy-e^x+e^y=0对x求导则(xy)'=1*y+x*y'(e^x)'=e^x(e^y)=e^y*y'所以y-e^x+(x+e^y)y'=0y'=(e^x-y)/(x+e^y)所以dy/dx=(e

x^(x^x)*(x^x*(log(x)+1)*log(x)+x^x/x)x/x\(x)|xx|即x|x(log(x)+1)log(x)+----|\x/

3、e^(xy)=2x+y^3,两边取微分d[e^(xy)]=d[2x+y^3]ye^(xy)dx+xe^(xy)dy=2dx+3y^2dy[xe^(xy)-3y^2]dy=[2-ye^(xy)]dx

再问：求详解谢谢再答：

x^20*y^15*z^5=32x^40*y^30*z^10=1024x^8*y^6*z^2=五次根号1024=4

2的x次方=8的y+1次方2的x次方=2的3（y+1）次方x=3（y+1）=3y+3----------------（1）81的y次方=9的x-5次方3的4y次方=3的2（x-5）次方4y=2（x-5

答：先求x^x的导数.记z=x^x,则lnz=xlnx.(lnz)'=(xlnx)'z'/z=lnx+1所以z'=(x^x)'=(lnx+1)*x^xy=x^(x^x),则lny=(x^x)lnx(l

z^x=y^z,隐函数F(x,y,z)=z^x-y^zFx=lnz*z^xFy=-zy^(z-1)Fz=x*z^(x-1)-lny*y^zбz/бx=-Fx/Fz=-(lnz*z^x)/(x*z^(x

解原式=(x^2+y^2)-(xy)^2=(x^2+xy+y^2)(x^2-xy+y^2)

x∈（-∞,0）∪（1,2）

[x^m]^n=x^(mn)(xy)^m=x^m*y^mx^(2y)=(x^2)^y(2x)^y=2^y*x^yx^(3y)=(x^3)^y(3x)^y=3^y*x^y

-(x+y)的10次方÷（x+y)的7次方÷（x+y)的2次方=-（x+y）^(10-7-2)=-(x+y)

两边同时取自然对数,得：y*ln(sinx)=x*ln(cosy)两边同时对x求导,得：y'*ln(sinx)+y*cotx=ln(cosy)-y'x*tany解y'得：dy/dx=y'=[ln(co

(x—y)的2次方×（x—y)的5次方×（y-x)=-(x-y)的2次方×（x-y)的5次方×（x-y)=-(x-y)的(2+5+1)次方=-(x-y)的8次方

(1+x^2)e^yy'-2x(1+e^y)=0令u=1+e^y则u'=e^y*y'代入方程得：(1+x^2)u'-2xu=0因此有：du/u=2xdx/(1+x^2)即：du/u=d(x^2)/(1