Determine which of the following expressions are exact differentials: (a) df = (y + z)dx + (z + y)dy + (x + y)dz (b) df = 2xy dx + 2yz² dy – (1 – x² – 2y²z)dz (c) df =z dx + x dy + y dz (d) df = (x' + 3x³y>z)dx + (y+ 2x'yz)dy + (x'y³)dz

Q: Find the derivative of the function. 3 In (x +8) 5-5x O A. dy %3D dx (x + 8)(5 – 5x)? О в. dy 15 -…

A: Given query is to find the derivative of the expression.

Q: B. Find the derivative of the function. 1. y = 3 2. f(x) = x + 1 3. f(t) = -2t + 3t- 6 4. f(x) = x?…

A: Since you have posted question with multiple subparts, here is the solution for the first three…

Q: Find the derivative. y=(x2+x)-3 OA. dy 3x5 (2-x³) dx (1+x³)3 OB. dy_3x4 (2-x³) (1+x³)3 dx 5C 31 ...

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Q: 3. If f(r, y) = x*y - 2x-4y, then the total derivative of f

A:

Q: Find the second, third, and fourth order derivatives of: y= f(x )= ax7 + bx3 + c y= f(x) = 3x/1-x…

A: It is simple derivative

Q: 1. x3 + y3 – 2xy = 0, find y'.

A:

Q: The percentage of female high school graduates who enrolled in college is given in the table below.…

A: Let x represent time(in years) since 1970, and let y represent the corresponding percentage of…

Q: 2. Find the derivative of each of the following functions: y = x¹2 (i) (ii) (iii) (iv) y = 3x ¹ y =…

A: 1) y=x12Differentiate w.r.t.'x'dydx=ddx(x12)We know thatddx(xn)=nxn-1Thereforedydx=12x11

Q: 4. Find all second order derivatives for the following functions. (a) f(x,y) = 2² + 3ry +2y², (b)…

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Q: 4- Calculate the second derivative of the function y = f(x) defined by the equation x³ + y3 +3xy +…

A: The given function is: x3+y3+3xy+3y2+6x+6y=0

Q: f2(x) = (4x + 5)°, fa(x)= (2x² +x)VI, fa(x) cos(3r) – 2 sin? x, COS

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Q: Find the derivative of y with respect to x.

A:

Q: Find all second order derivatives for z = 7ye4x. Zxx 0 Zyy = 3xy=2x =

A: The function is given by z = 7ye4x To determine: The expressions of zxx, zyy, zxy and  zyx.

Q: Find the derivative of the function. G(y) =  (y − 2)4 (y2 + 4y)5 G'(y) =

A: G(y)=(y-2)4(y2+4y)5 G'(y)=4(y-2)3(y2+4y)5+(y-2)4 5(y2+4y)4(2y+4)        =(y-2)3…

Q: Recall the derivatives of some common functions, and complete the table below Function Derivative…

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Q: Find all possible functions with the given derivatives. a. y' = 2x b. y' = 2x - 5 c. y'= 3x² - 2x -…

A: a y'=2x           b y'=2x-5           c y'=3x2-2x-5

Q: 12. a(t) a' (t) b(t) b'(t) -4 2 -3 -4 1 a. f(t) = a(t)b(t) Find f'(-4). b. g(t) = -3a(t)b(t) Find…

A:

Q: Consider the following. 1 - 2x² x42x² + 3 Let u(x) = 1 - 2x² and v(x) = x² − 2x² + 3. Find each…

A: We need to find derivative.

Q: I. Find the derivative of the following functions: a. f(r) = 23 + 6x b. h(r) = (3r + 4)2 c. y = Vr3

A: According to company rules, I need to solve first 3 subparts when multiple subparts are posted