Advertisements
Advertisements
प्रश्न
Find the partial dervatives of the following functions at indicated points.
g(x, y) = 3x2 + y2 + 5x + 2, (2, – 5)
उत्तर
g(x, y) = 3x2 + y2 + 5x + 2
`(delg)/(delx)` = 6x ++ 5
`(delg)/(dely)` = 2y
At (1, – 2)
⇒ `(delg)/(delx)` = 6(1) + (5)
= 11
`(delg)/(dely)` = 2(– 2)
= – 4
APPEARS IN
संबंधित प्रश्न
Let u = x cos y + y cos x. Verify `(del^2"u")/(delxdely) = (del^"u")/(del"y"del"x")`
Let u = x2y3 cos`(x/y)`. By using Euler’s theorem show that `x*(del"u")/(delx) + y * (del"u")/(dely)`
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 = 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:
Find the partial dervatives of the following functions at indicated points.
f(x, y) = 3x2 – 2xy + y2 + 5x + 2, (2, – 5)
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) = `(x^2 + y^2)/(xy) + 3z^2y`, find `(del"U")/(delx), (del"U")/(dely)` and `(del"U")/(del"z)`
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) = x2 + 3xy – 7y + cos(5x)
If v(x, y, z) = x3 + y3 + z3 + 3xyz, Show that `(del^2"v")/(delydelz) = (del^2"v")/(delzdely)`
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
