Advertisements
Advertisements
प्रश्न
Find the partial derivatives of the following functions at indicated points.
h(x, y, z) = x sin (xy) + z2x, `(2, pi/4, 1)`
Advertisements
उत्तर
h(x, y, z) = x sin (xy) + z2x
`(delh)/(delx)` = x[y cos (xy)] + sin (xy) + z2
`(delh)/(dely)` = x2 cos (xy)
`(delh)/(delz)` = 2zx
At `(2, pi/4, 1)`
`(delh)/(dely) = 2[pi/4 cos ((2pi)/4)] + sin ((2pi)/4) + (1)^2`
= `pi/2 cos (pi/2) + sin (pi/2) + 1`
= `pi/2 (0) + 1 + 1`
= 2
`(delh)/(dely) = (2)^2 cos ((2pi)/4)`
= `4 cos (pi/2)`
= 4(0)
= 0
`(delh)/(delz)` = 2(1)(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")`
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)`
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:
If q = 1000 + 8p1 – p2 then, `(del"q")/(del "p"_1)`is:
Find the partial dervatives of the following functions at indicated points.
g(x, y) = 3x2 + y2 + 5x + 2, (2, – 5)
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)`
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 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
