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 = `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 = `e^(x^2)` then `(del"u")/(delx)` is equal to:
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)`
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) = x2 + 3xy – 7y + cos(5x)
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 `(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)
