Advertisements
Advertisements
प्रश्न
If U(x, y, z) = `(x^2 + y^2)/(xy) + 3z^2y`, find `(del"U")/(delx), (del"U")/(dely)` and `(del"U")/(del"z)`
उत्तर
U(x, y, z) = `(x^2 + y^2)/(xy) + 3z^2y`
`(del"U")/(delx) = ((xy)(2x) - (x^2 + y^2)(y))/(xy)^2` + 0
= `(2x^2y - x^2y - y^3)/(xy)^2`
= `(x^2y - y^3)/(xy)^2`
= `(y(x^2 - y^2))/(x^2y^2)`
= `(x^2 - y^2)/(x^2y)`
`(del"U")/(dely) = ((xy)(2y) - (x^2 + y^2)(x))/(xy)^2 + 3z^2`
= `(2xy^2 - x^3 - y^2x)/(xy)^2 + 3z^2`
= `(xy^2 - x^3)/(xy)^2 + 3z^2`
= `(x(y^2 - x^2))/(x^2y^2)`
= `(y^2 - x^2)/(y^2x) + 3z^2`
`(del"U")/(delz)` = 0 + 6zy = 6zy
APPEARS IN
संबंधित प्रश्न
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 = `log (x^4 - y^4)/(x - y).` Using Euler’s theorem show that `x (del"u")/(del"x") + y(del"u")/(del"y")` = 3.
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 the indicated points.
`"G"(x, y) = "e"^(x + 3y) log(x^2 + y^2), (- 1, 1)`
For the following functions find the fx, and fy and show that fxy = fyx
f(x, y) = `(3x)/(y + sinx)`
For the following functions find the fx, and fy and show that fxy = fyx
f(x, y) = `tan^-1 (x/y)`
For the following functions find the fx, and fy and show that fxy = fyx
f(x, y) = `cos(x^2 - 3xy)`
If U(x, y, z) = `log(x^3 + y^3 + z^3)`, find `(del"U")/(delx) + (del"U")/(dely) + (del"U")/(del"z)`
For the following functions find the gxy, gxx, gyy and gyx
g(x, y) = log(5x + 3y)
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
Let V (x, y, z) = xy + yz + zx, x, y, z ∈ 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
