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- 3- Show that this function is differentiable for all and find its derivative f2) = f(x+ jy) = x* – 15x*y + 15x*y* - y6 + j(6x®y- 20x*y + 6xy")Given a 2-dimensional function T(x, y) = 2y² + sin(x) answer the following a) find the expression for the partial derivative ar dx use "pi" to denote. b) find the expression for the partial derivative or дуFind the indicated partial derivatives of: of ?x of ду || || -ly ƒ(x, y) = xye`
- c) Consider the third-order truncation error (O(Ax )³) with the step size Ax and also (-Ax ) then, subtract them and finally obtain a finite difference approximation for the first-order derivative of U respect x (Ux(x, t)). d) Consider the fourth-order truncation error (0(Ax )*) with the step size Ax and also (-Ax) then, add them and finally obtain a finite difference approximation for the second-order derivative of U respect x (Uxx(x, t)).af Consider the f unction g(t) = (², 2t) + 52(sin3t, t) express se ду g'(t) in terms of partial derivatives of f2OASIMMA UNV Y AL QASIMIA UNIVERSITY الجامعة القاسمية 5. a) Find the first order derivative of the following function. (6 Marks) y=x° In x b) Find the second higher order derivatives of the following function. P 25Q 10Q² +200 c) Find the partial derivatives? Y3D2X²+3xz85w-8z2
- (3,2), where h(u, v) = ue", u = q*, v = qr². Use the Chain Rule to evaluate the partial derivative o at the point (q, r) = dq (Use symbolic notation and fractions where needed.) dg\(g.r)Determine the second-order partial derivative for the indicated function f(c,y) = cos(2x² – 3y?) axdyla-3)compute all the 1st and 2nd partial derivatives of x2 sin (x+y)
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