If f dx and then there exists some E[a, b] such that g dz both exist and f is monotonic on [a, b], dx=f(a) dx+f(b) 8 dx.

Q: If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't…

A: It's nothing to do with f(z)=u(x,y)+iv(x,y). Here z be complex independent variable. Hence , z could…

Q: Evaluate: a In(x + y) e-y. dy dx

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Q: Find a if f(0) = 1, f(;) = }, f(1) = 2 and f(}) = f(}) = a give o f(x)dx = using the composite…

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

Q: dz/dy for z = e^xy

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Q: of and for the functions: dx dy H.W: Find 1. f(x, y) = (xy-1)² 3. f(x, y) = (x²-1)(y + 2) 2. f(x, y)…

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Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

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Q: If f and g are continuous on [a, b], then Lf(x)g(x)] dx f(x) dx (), 9. g(x) dx %3D a

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Q: If g(x) = ªſ*'[e'− In(2t+1)]dt, find g ''(x) . - dx -2 4 A + (2x + 1)2 Be-In(2x+1) 2 C (2x + 1)² 4 D…

A: Given that,      gx=ddx∫-2xet-ln2t+1dt

Q: Consider the function f(x, y) = 3 x² y + cos(e*'). Which one of the following is correct- Oyf x-x…

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Q: Find d3f where f(x, y, z) = ln(x + y − z) + cos(x2y)

A: As per the question we are given a multivariate function as : f(x, y, z) = ln(x + y − z) + cos(x2y)…

Q: (Note: This is a f(x) of Hyperbolic) e¯* + e* dx о ех — е х

A: We have to solve

Q: Q1-Use the chain rule to express dy / dx in terms of xand y: 1-1 a) y = аnd x = at 1= 2 1+1 b) y=1-…

A: Since you have posted multiple questions. I am answering the first one. Please post the question…

Q: Let w = 4e" dx /A dy + aeª dx ^ dz and n = 7e*Y dx + 8e² dy + eY dz, where a E R. Find the value of…

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Q: If z + In(e2x - e + e²) = 0 dz find at the point (0, 0) dx 2 0 -3 -2

A: see below the calculation and answer

Q: 1. Find -for each of the following: dx e) y =x* Inx f) In(x + y) = e*=y g) y = x2r-5

A: Here we have to find dy/dx .

Q: Find dy/dx for the following function:- (1) y= In(r+4)-xtan (4) y x*+1) (2) xy +xy x+ 3y (3) Iny e…

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Q: Q4 Find dy for all of : dx 3 x(x-2) 1- y = xvInx 2- у 3D x2+1

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Q: 3) Find dz dy for z = e

A: Solution: As per given date   z=exy  For finding dz/dy , we assume that 'x' is a constant.

Q: If g (x): A d dx [e' — In(2t+1)]dt, find g''(x) - -2 4 (2x + 1)² 4 B (2x+1)² Ⓒe*-In(2x+1) 2 D (2x +…

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Q: +! dy dx x dx A- If Z = d'y x dx x dx? Prove that Z.Z = xp -1% NI X

A: A Given Z=d2ydx2+1xdydx. We need to evaluate Z.Z. Consider Z.Z.…

Q: Evaluate /f/2e(*+у*+ dV over B where B - {(a, у, 2) : а? + у? +2? < 1}. Тake п %3 3. SSS 2e(z²+y° О…

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Q: Prove the general formula

A: Consider the given integral ∫dxx-ax-b First, decompose the partial fraction  1x-ax-b=Ax-a+Bx-b…

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.:…

A: We have the given function in x and y as 2xy-5x+3y3=-51 On differentiating both of the side with…

Q: Find dy/dx if y = x^3/2 by using the Chain Rule with y as a composition ofa. y = u3 and u =…

A: a) y=u3 and u=x     dydu=3u2anddudx=ddxx       =12x-12 So, dydx=dydu×dudx      =3u2×12x…

Q: If f(x,v) = ex In(5xy) find dy?

A: Given: fx,y=ex2ln5xy. To find: ∂2f∂y2 Solution: In partial derivative we differentiate with respect…

Q: f [Mesin(2x) dx = e$in(2x) + C, then the M is equal to- If

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Q: f(x) = | e 'cos(af(s))ds, 0<x< 1, 0 < a < 1, -SX

A: Given: f(x)=∫01e-sxcosαf(s)ds, 0≤x≤1, 0&lt;α&lt;1

Q: S dy S f(x, y)dx

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Q: 2- is the D.E:(3x² + y cosx )dx + ( sinx-4y )dy = 0 | a- - Exact b- linear D.E (show that)

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Q: fy = e*, y = 1 - e-x, and x = 0 ab- %3D

A: Given: - The curves of, y=e-x, y=1-e-x and x=0 about y=4.5 To find: - The volume of a solid is…

Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: dy B] If y = e" In(u) and u = V1-x2, Find dx

A: To find

Q: Show that f(t) dt ) dx (x - a)f(x) dx.

A: To prove: ∫ab∫xbftdtdx=∫abx-afxdx

Q: Let Dx be the linear transformation from C'[a, b] into C[a, b]. Find the preimage of the function.…

A: We have to solve above question and find preimage function

Q: Find dy of the expression (xy)* = e %3D dx

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Q: dy (a) Find if y = (In x)=². dx

A: For (a), dydx=lnxx2'       =ex2lnlnx'        =ex2lnlnxx2lnlnx'        =ex2lnlnx2xlnlnx+xlnx…

Q: dy at x=0. dx If y = (3x² + 4x + 5)(e* – cos 2x), then find %3D -

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Q: When reduced to a linear DE of order one in z, the Bernoulli's equation +y)=3x<y becomes dx dz 1 A…

A: Topic  =Differential equation Correct option  = A

Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.: y2 - 8x3 = -55; dx/dt…

A: y2-8x3=-55, dx/dt=-4x=2,y=3

Q: " dy_ x +x*e prove that dx Q: If x =k (1+e II

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Q: e of the function g(x y, z) = 1/xz + e%.

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Q: Suppose y is a function of x. Which of the following is d(x^3y) dx ? * 3x^2y + x^3dy dx 3x^2y 2x^3dy…

A: Givendx3ydx

Q: (1) So“ dx let t=x o Vx

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Q: of of For the function f(x,y) = In (x+ 3y), find and dx df of ду II

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Q: Which of the following is a linear ordinary D.E.? (d³y' I. dx3 dy + 2- = sin x dx II. dx d+ ( + = In…

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Q: In x Find y' if y = e3 1 – 4 In x Based on your work from (a), evaluate - dx. -5

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Q: Suppose that f (0) = 1, f(0.5) = 2.5, f(1) = 2, and f(0.25) = f (0.75) = a. Using trapezoidal rule…

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Q: dy If y = e" In(u) and u = V1-x2, Find dx

A: y = eu ln(u)       and   u = 1-x2 dydx = ?

Q: dy If y= f(u) = vu and u=g(x) = 7+x cos x , then find dx as a function of x using the chain rule dy…

A: If y=f(u)=u and u=g(x)=7+xcosx, then we have to find dydx using the chain rule.