b) Consider the second-order truncation error (0 (Ax)2) with the step size (-Ax) and then, obtain a finite difference approximation for the first-order derivative of U(x, t) respect x (Ux(x, t)).

Q: 3. Approximate the first order derivative of f(x)= x² + 2x at x = 3, using Forward, Backward and…

A: Formulas for differences are enclosed next page

Q: Find the direction derivative of f(x.y.z)-xy'z at the point p(3,2,1)in the direction towards…

A: To find the directional derivatives

Q: Find the weak derivative of f(x) = |x² − x + 1/5 on the - 1) interval (0,1).

A: 1.Given: fx=x2-x+15.To Find: The weak derivative of the given function on the interval 0, 1. Note-…

Q: Evaluate the derivative (r1(t) × r2(t)) where r1(t) = and r2(t) =. (Use symbolic notation and…

A:

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: find the first and the second derivative of these equation , first as a function of z then as a…

A: Given: Since you have asked multiple question, we will solve the first question for you. If youwant…

Q: -2 (a) Show that f'(x) using the definition of the derivative. (2x + 7)² (b) Find the equation of…

A:

Q: d) Consider the fourth-order truncation error (0(Ax )4) with the step size Ax and also (-Ax) then,…

A:

Q: c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and also (-Ax ) then,…

A: Both approximation is second order O((∆x)^2)

Q: cosh r – 1 · (xª4 + 2) +2). Compute the derivative of y = In | (2x + 1)

A: Given problem:-

Q: Use the derivative to find the critical point of f(x) = Ax² + Bx + C. Assume that A, B, and C are…

A:

Q: Let f(x) = e»in(²)+z² _ i) Find the x-values of the stationary points to the curve y = f(x), where 0…

A: The given function is  fx=esinx2+x2

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

A:

Q: 3- Show that this function is differentiable for all and find its derivative (2) = f(x+ jy) = x*-…

A: The necessary and sufficient condition for a complex function f(z)=U+iV  (where U,V are the real and…

Q: Let f(z) = (-6z— 4) (9z — 1)

A: f(z)=(−6z−4)(9z−1)

Q: What is the value of the first order derivative of the closed function given as…

A:

Q: c) Consider the third-order truncation error (0 (Ax )³) with the step size Ax and also (-Ax) then,…

A: The truncation error is of order O∆x3 The step length are ∆x, -∆x

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

A: Explanation: