Advertisements
Advertisements
प्रश्न
If v(x, y, z) = x3 + y3 + z3 + 3xyz, Show that `(del^2"v")/(delydelz) = (del^2"v")/(delzdely)`
Advertisements
उत्तर
v(x, y, z) = x3 + y3 + z3 + 3xyz
`(del^2"v")/(delydelz) = del/(dely) [(del"v")/(delz)]`
= `del/(dely) [3z^2 + 3xy]`
= 3x .........(1)
`(del^2"v")/(delzdely) = del/(delz) [(del"v")/(delz)]`
= `del/(delz) [3y^2 + 3xz]`
= 3x .......(2)
From (1) and (2)
⇒ `(del^2"v")/(delydelz) = (del^2"v")/(delzdely)`
APPEARS IN
संबंधित प्रश्न
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 u = `e^(x^2)` then `(del"u")/(delx)` is equal to:
If q = 1000 + 8p1 – p2 then, `(del"q")/(del "p"_1)`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) = `tan^-1 (x/y)`
For the following functions find the gxy, gxx, gyy and gyx
g(x, y) = xey + 3x2y
For the following functions find the gxy, gxx, gyy and gyx
g(x, y) = log(5x + 3y)
For the following functions find the gxy, gxx, gyy and gyx
g(x, y) = x2 + 3xy – 7y + cos(5x)
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 w(x, y) = xy + sin(xy), then Prove that `(del^2w)/(delydelx) = (del^2w)/(delxdely)`
A from produces two types of calculates each week, x number of type A and y number of type B. The weekly revenue and cost functions = (in rupees) are R(x, y) = 80x + 90y + 0.04xy – 0.05x2 – 0.05y2 and C (x, y) = 8x + 6y + 2000 respectively. Find the profit function P(x, y)
A from produces two types of calculates each week, x number of type A and y number of type B. The weekly revenue and cost functions = (in rupees) are R(x, y) = 80x + 90y + 0.04xy – 0.05x2 – 0.05y2 and C(x, y) = 8x + 6y + 2000 respectively. Find `(del"P")/(delx)` (1200, 1800) and `(del"P")/(dely)` (1200, 1800) and interpret these results
Let V (x, y, z) = xy + yz + zx, x, y, z ∈ R. Find the differential dV
