Advertisements
Advertisements
Question
For the following functions find the gxy, gxx, gyy and gyx
g(x, y) = x2 + 3xy – 7y + cos(5x)
Advertisements
Solution
gx = `(del"g")/(delx) = 2x + 3y - 5 sin(5x)`
gy = `(del"g")/(dely) = 3x - 7`
gxx = `2 - 25 cos(5x)`
gyy = 0
gxy = `del/(delx) ((del"g")/(dely))`
= `del/(delx) (3x - 7)`
= 3
gyx = `del/(dely) ((del"g")/(delx))`
= `del/(dely) (2x + 3y - 5 sin(5x))`
= 3
APPEARS IN
RELATED QUESTIONS
If z = (ax + b) (cy + d), then find `(∂z)/(∂x)` and `(∂z)/(∂y)`.
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 u = `e^(x^2)` then `(del"u")/(delx)` is equal to:
Find the partial dervatives of the following functions at indicated points.
f(x, y) = 3x2 – 2xy + y2 + 5x + 2, (2, – 5)
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 indicated points.
h(x, y, z) = x sin (xy) + z2x, `(2, pi/4, 1)`
For the following functions find the fx, and fy and show that fxy = fyx
f(x, y) = `tan^-1 (x/y)`
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) = xey + 3x2y
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)`
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
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
