Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y), where x = 8r cos(0) and y = 8r sin(0), find the following. (a) az ar əz ər (b) az де (c) дz де - = a2z ?re a2z ?re ?х дz ?x = + C ])+ 1). + ду дz ду 13. (L + ду 1) a2z DG-)-( дz ?х a2z ?у?х

Q: 3) у %3D 2u* + 1 x = 5u? – 5u -

A:

Q: Let h = fog where ƒ : R² → R and g: R² R² is defined by g(x, y) = (3x²y, x – 2y). Find the…

A: Letandfind the derivative

Q: (b) Find the first order partial af and ду af Əx ay for the derivative f(x y) = 2x² sin(x+ )…

A: To find the df/dx of partial first order differential we differentiate function with respect to x…

Q: the derivatives of y with respect to x: y = xe* – ex y = e(1x+) %3D y = e*(sin x + cos x) %3D y =…

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: a) z=cos² (3 xy) onde x=p+eº ey=p²-2e³8 b) z=4x³y onde x=3p²+0² e y=p²-40²

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Q: Find the directional derivative Du f(p) of the following function f

A: Given

Q: Find the derivative (dy/dx) of the following functions: h) у%3D Зx7 —7х3 + 21x2 - i) y = (x² +…

A: Since you have asked multiple questions in a single request, we will be answering only the first…

Q: 3) f(t) = t*e?t %3D

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: 12. Find the second derivative for the function f (x)=4x+12x²-20x-18 and solve the equation f"(x)=0.…

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Q: Use implicit differentiation to find az/ax and az/ay. x² + 4y² + 3z² = 5 ala ala дz ?х ду || ||

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: Suppose (-8, 6) is a critical point of a function f with continuous second derivatives. If fra (-8,…

A:

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: f(«, у, 2) — sec (9г + 3уг) fa = | fy = f: = ||

A:

Q: (x³ + bx + a, xs-1 lbx? - Let f(x) = .Then the values of a and b so that the %3D -a, x >-1…

A: The function is: f(x)=x3+bx+a, x≤-1bx2-a,      x>-1 So, the function is continuous at x=-1 if…

Q: e) s = cos (1– 21) -2 4t f) y = t+1, .2 x + x g) y =

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Q: Find y as a function of a if y(0) = 12, y(0) = 21, y"(0) = 18. y(x) = y" 16y" +63y = 144e²,

A: Given: y'''-16y''+63y'=144ex y0=12 y'0=21 y''0=18 To find: Solution to the given differential…