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
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).
Let u = x cos y + y cos x. Verify `(del^2"u")/(delxdely) = (del^"u")/(del"y"del"x")`
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 = `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) = `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)`
If V(x, y) = ex (x cosy – y siny), then Prove that `(del^2"V")/(delx^2) + (del^2"V")/(dely^2)` = 0
If w(x, y) = xy + sin(xy), then Prove that `(del^2w)/(delydelx) = (del^2w)/(delxdely)`
If v(x, y, z) = x3 + y3 + z3 + 3xyz, Show that `(del^2"v")/(delydelz) = (del^2"v")/(delzdely)`
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
