iv) if zx = (y)¯1 then zx/Zy %3D

Q: z = e4x + y ln(x), find zx and zy.

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Q: 1. S 2. [x²e²² dx 3. [sec* (x) dx 4. fxinx dx 5 ( x50x² dv x arccos x dx 6. Jese² (3x) dx 7. fx³ež…

A: Since multiple questions are asked, I am answering first question

Q: /1- (z² + y²) dz dy dæ ) Evaluate

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Q: Find y': y = ez² + 3x² + e²e Oy = e + 3x ln x + e²ex Oy' = e + 3x²-1 Oy = e + 3x² In a Oy = e +…

A: Given y=e12x+3xe+e2e Given query is to find the derivative y'

Q: x²V4x +1 dy then dx If y = In (x³ + 5)3

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Q: Minimize S = xy + xz + yz subject to xyz = 3 v

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Q: The integrating factor of the given DE are already given below. What is the value of “n”…

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Q: f(x, y) = log, (3x) fe dy In(3x)/(yln(y)2)^2 ||

A: Topic- partial differential

Q: 3t y" – 3y' – 4y = e|variationof parameters

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Q: 2 / y xx lnx xy + y = In

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Q: dy = ky dx x = eky y = e-kx Option 2 O Option 4 O y = ekx x = e-ky Optio n 2

A: The given equation is dy/dx=ky.

Q: n/3 SS ycos(xy)dydx= - π/ 3

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Q: Compute ∆y and dy for y = x^2 − 4x when changes from x = 3 to x = 3.5.

A: Topic:- application of derivatives

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Q: Find * dy ,If y 3 dx + x O x^2 + x O x^3 + x^2 +1 O x^2 + x + 1 O 3x^2 + 2x + 1

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Q: S S§y²cos(xy)dydx

A: we have given,                 ∫x =0x=1∫y=0y=π4y2cos(xy)dydx After arrangement,…

Q: X = e not inelude th degreo QUmbelin

A: The triangle is shown in diagram ,

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Q: S S* e*(y + 2z) dz dy dx

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Q: b) ƒ(x,y) = ln(3x + 5y).

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Q: 2e | 3జy S S dy da = Vsin(zy)

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Q: зхе-МХxcos(Nx) 5- a. Differentiate: y = M csc(Nx)+Nx

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Q: x^2(lnx-lny)dy=y(ylny-ylnx)dx

A: Explained below

Q: 9. Find the General and Particular solution of = 4y ; y= 3,when x dx

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Q: y et 2x *Sec2X Pinel dy o

A: By using these differential formulas that are ddxex=ex, ddxax=axlnx where a is constant,…

Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = ln (x + 2y + 3z)

A: Given, ƒ(x, y, z) = ln (x + 2y + 3z)

Q: 5. S , dz dy dx 2 c3

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Q: dx + 6x = 3yæ y- dy 1 1 x = (x – a²C)³ (y – y²C)³ Option 1 Option 2 1 1 y = (x + x²C)³ x = (y +…

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Q: General solution of (ylny − e¯xy)dx + (² + xlny) dy = 0

A: Let's solve given diffrential equation.

Q: 23) Fnd yp of yll-ly'+hy=48+2tesin2t (Oo not evaluate cefficients)

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Q: Z eXZ 4. xyz dydx dz

A: Solution:

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Q: 'a-x - dx atx valuate

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Q: dy 1+y+1

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Q: .1 S S, x(x² + y²)²/3dydx

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Q: 4. ydx + x(Inx - Iny - 1) dy = 0, when x = 1, y = e

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Q: - 3-z2-y 2. Evaluate L* L z dz dy dx -5+x²+y²

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Q: 5 2 S- 10 Vx+y dy dx 5 2 y dy dx = (28 - 10/3) 10 VX+y 3.

A: given itegralI=∫15∫02yx+y2dydx

Q: The integrating factor of the given DE are already given below. What is the value of "n" yly²-x-8)dx…

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Q: 2y4 y3 – y2 + y – 1 dy = y² + 2y + In ly – 1| -in ly2 + 1| - y +C

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Q: • The integrating factor of the given DE are already given below. What is the value of "n" y²dx…

A: In order to find the value of 'n', follow the following steps.

Q: 16. If x x y and y x z, then how is x proportionally related to z?

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Q: 5. ydx - (x +3y')dy = 0 Ans. x = 6y In C

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Q: 3x 6 1 -In xy dx e-In √x dx +dy +=dx = e-mxx y X

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Q: dx + 6x y- dy 1 y = (x – a²C)³ (y – y²C)³ Option 1 Option 2 1 1 (y+ y²C)³ (x + x²C)³ Option 3 Option…

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Q: The integrating factor of the given DE are already given below. What is the value of “n” 3y2dx…

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