Z=xsin(xy)的两个一阶偏导数-搜答案-拍题作业网

令z=1/y^4,则y'=-y^5z'/4代入原方程,化简得z'+4z=-4x.(1)∵方程(1)是一阶线性微分方程∴由一阶线性微分方程求解公式,得方程(1)的通解是z=1/4-x+Ce^(-4x)(

根据一阶全微分形式不变得dz=d(xf(x^y,e^xy)=f(x^y,e^xy)dx+xd(f(x^y,e^xy))=f(x^y,e^xy)dx+x[f1'd(x^y)+f2'(de^xy)]=f(

∂z/∂x=(∂f(u,v)/∂u)*(∂u/∂x)+(∂f(u,v)/∂v)*(∂v/&#

令u=x^2+y^2,v=xy得∂z/∂x=(∂f/∂u)(∂u/∂x)+(∂f/∂v)(∂

dz=[sin(xy)+xycosxy]dx+(x^2cosxy)dydz|(1,1)=(sin1+cos1)dx+cos1dy再问：先求dx，dy，详细过程谢谢再答：=sin(xy)+xycosxy

方程两边对变量x求导有d[sin(xy)]/dx=dx/dxcos(xy)*d(xy)/dx=1cos(xy)*(dx*y+x*dy)/dx=1cos(xy)*[y+x*(dy/dx)]=1所以：dy

∂Z/∂x=y*cos(xy)-2cos(xy)*sin(xy)*y=y*cos(xy)-y*sin(2xy)∂Z/∂y=x*cos(xy)-2cos(

对x求导,e^z*z'(x)=yz+xyz'(x),z'(x)=yz/(e^z-xy)对y求导,e^z*z'(y)=xz+xyz'(y),z'(y)=xz/(e^z-xy)

再问：可以再帮我答题吗，我这边有很多财富值可以给你再问：

z=(x^2)*ln(2xy),Zx=(2x)ln(2xy)+(x^2)/2xy*(2xy)'=(2x)ln(2xy)+xZxx=2ln(2xy)+(2x)/2xy*(2xy)'+1=2ln(2xy)

令u=xy,v=e^(x+y)Z'x=Z'u*U'x+Z'v*V'x=f'u*y+f'v*e^(x+y)Z'y=Z'u*U'y+Z'v*V'y=f'u*x+f'v*e^(x+y)

见下图

对两边分别求导,得dy/dx=-sin(xy)*(x*dy/dx+y)则dy/dx(1+sin(xy)*x)=-sin(xy)*y所以dy/dx=(-sin(xy)*y)/(1+sin(xy)*x)

f1表示f对第1个变量求导数,其余类推.∂μ/∂x=f1+f2(y)+f3(yz+xy∂φ/∂x)=f1+yf2+y(z+x∂φ/ͦ

(1)z=ln(tanx/y)dz/dx=1/(tanx/y)*(sec²x/y)=sec²x/tanxdz/dy=1/(tanx/y)*(-tanx/y²)=-1/y(

(注:偏导数的符号姑且用"d"表示)dz/dx=1/{y[2(x/y)^0.5]}(算z对x的偏导数时,把y看成是一个常数即可)dz/dy=-x/{y^2*[2(x/y)^0.5]}(算z对y的偏导数