Advertisements
Advertisements
Question
If z = (ax + b) (cy + d), then find `(∂z)/(∂x)` and `(∂z)/(∂y)`.
Advertisements
Solution
Given, z = (ax + b) (cy + d)
Differentiating partially with respect to x we get,
`(∂z)/(∂x) = ("c"y + "d") ∂/(∂x) ("a"x + "b")` ...[∵ (cy + d) is constant]
= (cy + d) (a + 0)
= a(cy + d)
Differentiating partially with respect to y we get,
`(∂z)/(∂y) = ("a"x + "b") (∂)/(∂y)`(cy + d)
= (ax + b)(c + 0)
= c(ax + b)
APPEARS IN
RELATED QUESTIONS
Let u = x cos y + y cos x. Verify `(del^2"u")/(delxdely) = (del^"u")/(del"y"del"x")`
If u = 4x2 + 4xy + y2 + 4x + 32y + 16, then `(del^2"u")/(del"y" del"x")` is equal to:
Find the partial dervatives of the following functions at indicated points.
f(x, y) = 3x2 – 2xy + y2 + 5x + 2, (2, – 5)
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
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 v(x, y, z) = x3 + y3 + z3 + 3xyz, Show that `(del^2"v")/(delydelz) = (del^2"v")/(delzdely)`
Let z(x, y) = x2y + 3xy4, x, y ∈ R, Find the linear approximation for z at (2, –1)
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
