xy=[tan(x^3+y^3)]^2Let z=x^3+y^3 => z'=3(x^2+y^2*y')xy'+y=2tan(z)*sec(z)^2*z'={sin(z)/[cos(z)]^3}*6(x^2+y^2*y')xy'-sin(z)*6y^2*y'/[cos(z)]^3={sin(z)*6x^2/[cos(z)]^3}-y=y'[x-sin(z)*6y^2]/[cos(z)]^3y'=[{sin(z)*6x^2/[cos(z)]^3}-y]/[x-sin(z)*6y^2]/[cos(z)]^3={6x^2*sin(z)-y*[cos(z)]^3}/[x-6y^2*sin(z)]
Question： For implicit function 2xy + eˣ⁺ʸ - 2 = 0, dy/dx|₍₀,₂₎ = ? ...
設F(x,y)= exp(2x-y)+cos(x^2+xy)-2-2y, 則 ∂F/∂x = 2 exp(2x-y)- sin(x^2+xy) *(2x+y) ∂F/∂y = - exp(2x-y) - x sin(x^2+xy) - 2 (x,y)=(0,0)處, ∂F/∂x=2, ∂F/∂y= -3 兩項均不為0, 故y可視為x之函數, x亦可視為y之函數, 且 dy/dx = -[∂F/∂x] / [∂F...
1.dk/dj=3j^2+2/j^2-(cscj)^2 dk/dx=0 dk/dy==0 2.dA/dx=2[sec(x^2+y)]^2 dA/dy=[sec(x^2+y)]^2 dA/dt=0 3.這一題你題目應該打錯了，括號括錯地方了，我幫你改成正確的。 d[(x^2)y-y/(3x)+2z]/dx=2xy+y/3x^2 d[(x^2)y-y/(3x)+2z]/dy=x^2-1/3x d[(x^2)y-y/(3x)+2z]/dz=0
1.x^3-y^2=6xydefine y'=dy/dx,x'=dx/dy3x^2-2yy'=6y+6xy'3x^2-2yy'=6y+6xy'y'(2y+6x)=3x^2-6yy'=dy/dx=(3x^2-6y)/(2y+6x)3x^2x'-2y=6yx'+6xx'(3x^2-6y)=6x+2yx'=dx/dy=(6x+2y)/(3x^2-2y)2. 3. 遵此要領Find d^2y/dx^2for the following problems(with no dy/dx invovled)1.3x^2-4y^2=76x-8yy'=0y'...
3-dim: 顯函數(explicit fn.) z= f(x,y) 隱函數( implicit fn.) f(x,y,z)=0 參數式(parametric eq.) (x(u,v), y(u, v), z(u,v)) 4-dim: 顯函數...
根據你提供的資料檔，程式如下： program main implicit none integer*4 i, n, imax, imin real*8 x(5000), y(5000), z(5000), sum, sum2, avg, zmax...
...the radius of convergent ; 發散:divergence 連鎖法則: the chain rule 隱函數與相關變率: Implicit Differentiation and Related Rates 反函數: Inverse...
