Advertisements
Advertisements
प्रश्न
For the following functions find the gxy, gxx, gyy and gyx
g(x, y) = xey + 3x2y
Advertisements
उत्तर
`(del"g")/(del"y") = "g"_x = "e"^y + 6xy`
`(del"g")/(dely) = "g"_y = x"e"^y + 3x^2`
gxx = `(del^2"g")/(delx^2)`
= `del/(delx) [(del"g")/(delx)]`
= `del/(delx) ["e"^y + 6xy]`
= 0 + 6y
= 6y
gyy = `(del^2"g")/(dely^2)`
= `del/(dely) [(del"g")/(dely)]`
= `del/(dely) [x"e"^y + 3x^2]`
= `x"e"^y`
gxy = `(del^2"g")/(delxdely)`
= `del/(delx) [(del"g")/(dely)]`
= `del/(delx) [x"e"^y + 3x^2]`
= `"e"^y + 6x`
gyx = `(del^2"g")/(delydelx)`
= `del/(dely) [(del"g")/(delx)]`
= `del/(dely) ["e"^y + 6xy]`
= `"e"^y + 6x`
APPEARS IN
संबंधित प्रश्न
If z = (ax + b) (cy + d), then find `(∂z)/(∂x)` and `(∂z)/(∂y)`.
If u = exy, then show that `(del^2"u")/(delx^2) + (del^2"u")/(del"y"^2)` = u(x2 + y2).
Verify Euler’s theorem for the function u = x3 + y3 + 3xy2.
Let u = x2y3 cos`(x/y)`. By using Euler’s theorem show that `x*(del"u")/(delx) + y * (del"u")/(dely)`
If u = 4x2 + 4xy + y2 + 4x + 32y + 16, then `(del^2"u")/(del"y" del"x")` is equal to:
If u = x3 + 3xy2 + y3 then `(del^2"u")/(del "y" del x)`is:
If q = 1000 + 8p1 – p2 then, `(del"q")/(del "p"_1)`is:
Find the partial derivatives of the following functions at indicated points.
h(x, y, z) = x sin (xy) + z2x, `(2, pi/4, 1)`
If U(x, y, z) = `(x^2 + y^2)/(xy) + 3z^2y`, find `(del"U")/(delx), (del"U")/(dely)` and `(del"U")/(del"z)`
For the following functions find the gxy, gxx, gyy and gyx
g(x, y) = log(5x + 3y)
Let w(x, y, z) = `1/sqrt(x^2 + y^2 + z^2)` = 1, (x, y, z) ≠ (0, 0, 0), show that `(del^2w)/(delx^2) + (del^2w)/(dely^2) + (del^2w)/(delz^2)` = 0
If V(x, y) = ex (x cosy – y siny), then Prove that `(del^2"V")/(delx^2) + (del^2"V")/(dely^2)` = 0
Let z(x, y) = x2y + 3xy4, x, y ∈ R, Find the linear approximation for z at (2, –1)
If v(x, y) = `x^2 - xy + 1/4 y^2 + 7, x, y ∈ "R"`, find the differential dv
Choose the correct alternative:
If g(x, y) = 3x2 – 5y + 2y2, x(t) = et and y(t) = cos t then `"dg"/"dt"` is equal to
