(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: b) Consider the second-order truncation error (0 (Ax)2) with the step size (-Ax) and then, obtain a…

A: The truncation error is O∆x2 and the step size is -∆x

Q: 4. Determine the directional derivative of f(r, y, z) = xe"+rsinz+a²y at the point (2,0, ) in the…

A:

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: Derivatives Show that d(y,v)/dv = (1 – v?/c²)-2 for y, = 1/V1- v² /c².

A:

Q: 3. Find the derivative of y with respect to x in the following functions : 18x'y (ans.: (3x-2) a)…

A:

Q: Calculate the derivative of t2 -k 3 - t F(t) = cos(t) i + 3e2t+2j + |

A:

Q: If we are getting the partial derivative of f(x,y) with respect to x, we are letting the y variable…

A: hello greetings from bartelby.i am here to help you.

Q: Find y as a function of a if y(0) = -2, (0) = 9, '(0) = -62. y(x) = y" - 4y" -y + 4y = 0,

A: Given that y''' -4y'' - y' + 4y = 0 ,   y(0) = - 2 y(0) = 9 '(0) = -62.

Q: Calculate the second derivative of the function y = f (x) defined by the equation x3 + y3 +3xy +…

A: Explanation:

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.