Advertisements
Advertisements
Question
Find the partial dervatives of the following functions at indicated points.
g(x, y) = 3x2 + y2 + 5x + 2, (2, – 5)
Solution
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
RELATED QUESTIONS
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")`
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)`
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:
Find the partial derivatives of the following functions at indicated points.
h(x, y, z) = x sin (xy) + z2x, `(2, pi/4, 1)`
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) = `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)`
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)
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
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
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
