(3) Consider the derivative dz = 2xydx + (x² + 2y)dy Evaluate whether this is a total derivative, by integrating along straight lines (i) (x1, y1) → (x2, Y1) then (x2, y1) → (xX2, Y2); and (ii) (x1,Y1) → (X1, Y2) then (x1, y2) → (x2, Y2).

Q: Find the directional derivative of the function at the point P(2,1) in the following direction:…

A: The given function is:f(x,y)=3x2y-2xy2+y3-9P=(2, 1)Direction vector:  v=3i-5j

Q: Let f (x) = 2x4 + 2x3 + 2x2 + 5x + 2. Fill in the missing coefficients for the derivative of f: x* +…

A: Given that :-  f is function of x f(x) = 2x⁴ + 2x³ + 2x² + 5x + 2 * We have to find  f '(x)   For…

Q: xy Find all second order derivatives for r(x,y)= 4x +9y

A: The given function is

Q: Find the derivative of the function f (, y, z) = 4ay z at the point (4, 64, 16) in the direction of…

A:

Q: (u(t)xv(t)) = 00)

A: Given that the expression

Q: 9) y = e4x² + x A) dy dx 8xe2x + 1 B) dy - 8xex2 dx %3D + 1 C) dy dy - 8xe4x2 dx — 8хе + 1 %D D) + 1

A: We have to find

Q: Calculate the derivative of the function. Then find the value of the derivative as specified. dr 6.…

A:

Q: 5z²)* 4/3 %3D

A: (3). The function is given by Hz = 1-5z243 To evaluate: The derivative of the function.