3. Find d, where ; a) cos(xy)- (x+y) (x+ =2 + e

Q: Given z = (e-2) (siny), find dr -2x O-2 e 2² (cos y) O-2 e 2 (sin y) O-2 e 2 (sin y) +e-2 (cos y)…

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Q: Given y= 5e3X + sin x, -is dx A) 5e3x + cosx B 5e3x – cosx 15e3x + cosx D 15е3х — сosx

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Q: 10. y = C, cos 4x + C2 sin 4x + C3xcos 4x + C4xsin x + C5; C, to C5 are arbitrary constants

A: Since their are 5 arbitrary constants so the differential Equations will be of order 5. We find the…

Q: 3. Find dy, where; a) cos(ry) - e 2 elx+y). b) ė?+ Ptany =4, u= xlax (use chain rule)

A: We have to find the derivative

Q: -п/2 сп/2 w L cos dz dy de (ху

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Q: 2.) If H (y) = cos y – sin y, find H (0), H (n),H (T), and also show that H. n+ x) = H (n - x) = -H…

A: The solution is given as

Q: if(r, y) = e sin 8y, then fry is given by: 2z O 16 e* sin 8y O – 16 e2* sin 8y O 16 e2 cos 8y O – 16…

A: Solving differential equations . To solve the differential equations.

Q: Solve (by separation of variables) the following problem du = 0 ; x E R , t> 0, t > 0, - и(х,0) =…

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Q: (a) If y = tan x, prove that y = 2(y2 + 1)(3y2 + 1). (b) Find y' for y cos(sin?x). %3D %3D dy (c) If…

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Q: (d^2 y)/〖dt〗^2 +16y=cos ⁡t

A: The given equation is; (d2 y)/(dt2) +16y=cos ⁡t

Q: 3. If G = (2x²y – x*)î + (e*y + y sin x)j+ (x² cos y)k, find: %3D дхду

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Q: Practice by Evaluating 1 VI-x² cos(a² + y³)dydx 0.

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Q: y' – 3y + 2y = cos(e-")

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Q: If f(x,y)=log, (cos²(e* ) +si f(x,y) is ây ôx + sin(x+ y) then %3D

A: Given that: fx,y=logecos2ex2+sinx+y To determine ∂∂y∂∂xfx,y

Q: B. and , if z = (x² + y²)³/2, and r = e-" sin v, y = e¬u cos v. В. %3D

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Q: 1. Lif f(x,y,2)=2exp(-5xyz)cos(15z) Find ôxôz

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Q: /hich of the following does not require the use of the dy nain rule to find ? dx A y = cos1 (10x –…

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Q: Given the following DE (cos 2y – 3x?y?)dx + (cos 2y – 2x sin 2y – 2xy)dy = 0 -

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Q: Solve the following DE: [2x+ ycos(xy)] dx+ x cos(xy) dy = 0

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Q: If z=In/x2+y2 +- tan 2 then the numerical value of + is equal to..... dy? dx

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Q: 3. Let V = e" cos(qr), with p = x In(xyz), q = z cos(ry) and r = 2 tan-(y). By using the chain rule,…

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Q: 3. Let V = e cos(qr), with p = x ln(xyz), q = z cos(лy) and r = 2 tan−¹(y). ᎧᏙ By using the chain…

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Q: Given that: z = y sin(2x) + (1+x²)e* + cos x tan¬1(y* + 1) In(y6 + 137)

A: z=ysin2x+1+x2ex+cosxtan-1y4+1lny6+137 Differentiating wrt x, we have…

Q: Q3 Suppose that w = x² + y² + z² x = e" cos 0 ,y= e"sin0 ,z = re® aw аnd ar aw Find дө

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Q: 5. If z = f(x, y), where x = r cos 0 and r sin 0, find z and and hence show that: (). (-(( 2 2 dz dz…

A: To find the partial derivatives of the following function in two variables by chain rule.

Q: sin(iny)dy is equal to * y (A none of these cos(ny) + C y cos(Iny) + C (D) -cos(iny) + с cos((ny) +…

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Q: L(cos at) = %3D s2 - a2 صواب İhi O

A: Given that  L(cosat)=s/(s^2-a^2) To find the condition is true or false

Q: Suppose that w = x² + y? + z², x = cos 0, y = sin 0, z = tan 6. Use the chain rule to find dw when 0…

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Q: d. t sin 2 dt COS dx 3

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Q: Let y=9 In(cos(a). in(co(e*). dy = AeBt sinC (e6t) Then dt cosº (e6t) where A = B = C = D =

A: Given expression y=9lncose6t Differentiate the above expression w.r.t "t" dydt=9ddtlncose6t Recall…

Q: Determine c, and c2 so that y(x) = c, sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

A: Consider the function: yx=c1sin 2x+c2cos 2x+1. Calculate c1 and c2. Given yπ8=0 and y'π8=2.   Since…

Q: If f(z, y) = e sin 8y, then fzy is given by: O 16 e sin 8y 16 e sin 8y O 16 e cos 8y 27 16 e cos 8y

A: We can solve it by taking partial derivative of both side two times as below

Q: The value of 'b' for which u(x, y) = ebx cos 5y is harmonic

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Q: 3. Given that z = e" cos (), u = 4e2" – sin 2y, v = e" + n tan r. COS - Use chain rule to find dz/ðx…

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Q: 5 Find *: (a) y = cos(11x + 2x) dy

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Q: Given f(x.y) = e X cos y, Evaluate fx(2,0) e2 cos 2 O sin 2

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Q: y" – 3y' + 2y = cos(e-*)

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Q: Given the implicitly defined function 6. cos (2*y) – y* - cos(2r) – y? dy and dr dr find at the…

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Q: Let 1 = , x² cos(x) dx. The approximation of I using the two-point Gaussian quadrature formula is:

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Q: cos (y) C = 3x2

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Q: (b) Determine J cos(x²) 2x dx by using substitution method.

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Q: 3. Find (in simplest form) dy/dx: y=In(4x² – 3) cos.x b. y=e0s* а.

A: We have to find dydx: a.  y=ln4x2-3b.  y=ecos x We know the formula of derivatives, dxndx=nxn-1d…

Q: Given G(x, y) = y* sin(2x)+x² ( x0 º – cos(y²))' find Gyyyxxxy „10 ууххху

A: Consider A(x,y)=y4sin2x and B(x,y)=x2y10-cosy27 then G(x,y)=A(x,y)+B(x,y).Therefore…

Q: Determine cı and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

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Q: (e) y' +2y : = cos(2x)

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Q: Given that: z = y sin(2x) + (1+x²)e* + cosx tan¬(y* + 1) In(y® + 137)

A: ∂z/∂x  is the partial differentiation of function z with respect to x, keeping other variables…

Q: 1. Please answer the following questions. a) [x-In (4x²) dx b) ſe* *. cos (2x) dx c) [In (x² +2) dx…

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Q: Find d2y/dx2 implicitly in terms of x and y 3xy − 4 cos x = −6

A: Find d2y/dx2 implicitly in terms of x and y 3xy − 4 cos x = −6

Q: (4) If z = f(r, y) where, a = e" cos v and y = e" sin v, show that (i) dz az e2u. (ii) az 2 2 dz -2u…

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