若dx/dt=5, dy/dt=4, x^3+y^3+z^3=3, 求当(x,y,z)=(1,1,1)时dz/dt 的值 各位大神求解答

dy/dx=(x^4+y^3)/xy^2

[y/(4+y^2)]dy=[x/((1-x^2)]dx;#{左右分别运用基础积分公式即可}

x^3+y^3+z^3=xyz求z对x与z对y的偏导数

先对等式两边求微d(x^3+y^3+z^3)=d(3xyz)3x^2dx+3y^2dy+3z^2dz = 3xydz+3xzdy+3yzdx (1)求z对x的偏导数,则y视为常量,dy/dz=0,(1)式转换为3x^2dx/dz+3z^2=3xy+3yzdx/dzdx/dz = (xy-z^2)/(x^2-yz)求z对y的偏导数,则x视为常量,dx/dz=0, (1)式转换为……别去解方程啦,观察原函数是对称的,所以把上面答案里x,y对端就行了(你非要解方程我也不拦着)dy/dz = (xy-z^2)/(y^2-xz)

dy/dx=5^(x+y)

解:∵dy/dx=5^(x+y) ==>5^(-y)dy=5^xdx ==>-5^(-y)/ln5=5^x/ln5-C/ln5 (C是积分常数) ==>-5^(-y)=5^x-C ==>5^x+5^(-y)=C ∴原方程的通解是5^x+5^(-y)=C.

u=x^3 y^3 z^3-3e^xyz 求全微分

du=3x²y³z³dx+3x³y²z³dy+3x³y³z²-3e∧xyz(yzdx+xzdy+xydz)

常微分方程组求解 dx/t=x^4-2xy^3 dy/t=2yx^3-y^4 discover what you can .

解:∵dx/t=x^4-2xy^3 dy/t=2yx^3-y^4(此题好像有错,应该是dx/dt=x^4-2xy^3 dy/dt=2yx^3-y^4.但无论怎样解法都一样. )∴dy/dx=(2yx^3-y^4 )/(x^4-2xy^3)==>dy/dx=(2(y/.

解二阶微分方程组dx/dt=x-3y dy/dt=3x y

y=2/3x-x^2+c

dx/dt=y+z,dy/dt=x+z,dz/dt=x+y.求解方程组,要过程,谢啦

dx/dt=y+z,dy/dt=x+z,dz/dt=x+y.求解方程组这里x, y, z是对称的,d(x+y+z)/dt = 2*(x+y+z), x+y+z = C*(e^(2t))故x=y=z = C*(e^(2t)).

设函数y=y(x)由方程x^2+5xt+4t^3=0 e^y+y(t-1)+lnt=1;求x=1时 dy\ dx - .

就是先用隐函数求导法得到dx/dt, dy/dt, 然后相除就得到dy/dx.x=1代入方程:x^2+5xt+4t^3=0,得: 1+5t+4t^3=0, 得:4t^3+4t+t+1=0, 得:(t+1)(4t^2-4t+5)=0,得t=-1 将t=-1代入方程:e^y+y(t-1)+lnt=1, 此时无意义.是不是题目抄错了?

求z=x^3ln(x^3+y^3)的一阶偏导数

z=x^3ln(x^3+y^3)dz=3x^2ln(x^3+y^3)dx+x^3*[1/(x^3+y^3)]*(3x^2dx+3y^2dy)=3x^2ln(x^3+y^3)dx+x^3(3x^2dx+3y^2dy)/(x^3+y^3)]=3[x^2ln(x^3+y^3)+(x^5)/(x^3+y^3)]dx+[3x^3y^2/(x^3+y^3)]dy

设方程组x+y+z=a,x^3+y^3+z^3=3xyz,求dy/dx,dz/dx

将z=a-x-y代入方程2得: x³+y³=3xy(a-x-y) x³+y³=3axy-3x²y-3xy² 两边对x求导:3x²+3y²y'=3ay+3axy'-6xy-3x²y'-3xy²-6xyy' 得:y'=(x²-ay+2xy+xy²)/(ax-x²-2xy-y²) 此即为dy/dx 类似地,将y=a-x-z代入方程2得: x³+(a-x-z)³=3x(a-x-z)z 两边对x求导: 3x²+3(a-x-z)²(-1-z')=3(a-x-z)z+3x(a-x-z)z'+3x(-1-z')z x²-y²-yz'=yz+xyz'-xz-xzz' 解得:z'=(x²-y²-yz+xz)/(xy-xz+y) 此即为dz/dx