1. Obtain the par hicul ar foluhon 4 DE . 9xy dy a. oy dx = ; uh en x= 2,y=1 b. 4xy dy = 2y (I+ y?) dx; when x- 2 ,y= ?

Q: dy sec (re ), y(In 4) = 3 / t dt

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Q: a.) Evaleiate. (6tanx dx

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Q: 9. If y = sinh 4t and r = sinh t, show that 2 dy (a) (1+2²) = 16(y? +1), dr dy (b) (1+x²)- dx2 dy…

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Q: If y = atan (0) „x =a sec (0) prove or disprove d'y 3 cot(0) 4a dx

A: y =a tan3θ   ,   x = a sec2θ     'y' is a function of 'θ' and 'x' is also      a function of…

Q: Evaluate (2х — у) dx + (х + 3у) dy. Jc C: arc on y = x>1² from (0, 0) to (4, 8)

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Q: So Simz So e" dz dy dx uate: e + Vē – 1

A: Please refer to the image below

Q: 22. Evaluate So Si S dx dy dz.

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Q: dy for y= In(In(2r')) dt

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Q: Given z = 17 In(t) and y = 289 t then fir dy d'y dx?

A: Differentiate given function

Q: If y=xtan(x) then dy at x = Tt is: dx

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Q: Evaluate Si S dz dæ dy 0. 4.

A: Here I am attaching image so that you understand each and every step.

Q: Given z = 3 In(t) and y = 9t then find dy dx dy dx2 |3|

A: givenx=3lnt,y=9t2

Q: Given y = ecos" a, at x = a dy > dx

A: Given that  y=e^(cos^3x)  To find the dy/dx at x=π/2

Q: What is the difference between dy dy and Ay Use an example y = 4x?+ eX to under stand. 4x2+ ex

A: In the given questioin we have to tell about the difference between dydx,∂y∂x and ∆y∆x. first we…

Q: Evaluate xy z? dx dy dz

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Q: Given z = 8t – 18 and y= 64 sin t dy (i) da dy (ii) dx?

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Q: Given x 13 In(t) and y = 169 t2 then find %3D dy dx dy dæ?

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Q: dy 3) Determine the of : In (ху?) %3D х у dx

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Q: B. Use Greens Theorem to evalute é yx dx + x*dy as shown bele Left Half of (0.5)

A: Introduction: Let C denote the positively oriented, smooth, and simple closed curve in a plane and D…

Q: Lind dy/dx O ztanag In 3 Funas Inx I + Inx

A: Consider the provided question, We need to find  dydx of the given function. (1) Given,…

Q: dy IS let y = (cos r)m " then de sin z

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Q: Find dy/dx in terms of a and y if arctan(x'y) = ry. dy %3D dx

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Q: Evaluate [y cos (3y) dy

A: We use integration by parts continuously. ∫f(y)g(y)dy =f(y)∫g(y)dy  - ∫df(y)dy(∫g(y)dy )dy Also note…

Q: -If x= cot- VE, y = ;, find dy dx'dx2 at t = 2.

A: We will use the formula (f(g(x))' = f'(g(x))g'(x)uv' = vu'-uv'v2 Given x = cot-1ty = 1t+1 Then dxdt…

Q: Find dy du dy and when y and u are defined as follows. du dx dx y = 3u² + 6 and _u = x² + 2

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Q: Given x 6 In(t) and y = 36 t2 then find %3D dy dx dy dx? ||

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Q: 1 If y = tanu, u=v--, and v= lnx, dy at x=e? dx what is the value of Select one: a. 0 O b. 1 1 C. d.…

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Q: Given that y + x + cos(xy) = 0. Show that dy/dx = ysin(xy)-1 /1-xsin(xy)

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Q: 7. Calculate dy/dx at the point indicated: f(0) = (7tan O, cos O), 0=/4

A: Here we will use the concept of parametric equation and Derivative of parametric ewyations

Q: Find d when y = 3 In(In(In(x))) dy dx

A: Here we can find the derivative as below

Q: - 403 y = cos dy %3D de

A: Given : y = cose-4θ3

Q: Show for Re(z) > 1 -dx = r(z) (2). et - 1

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Q: - arctan(e**) dx =? 1+e2kx A) (arctan(e*)In [cos(arctan(e*)| + S In [cos(arctan(e*)da]+ c kekz B)…

A: Let I=∫tan-1ekx1+e2kxdx where tan-1ekx=arctanekx Put tan-1ekx=t…

Q: If we have to check the DE (5-8y+4xy)dx = (x+2)'dy for Exact then My %3D

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Q: 4. Use Green's Theorem to evaluate | ay dx + (1 – ry) dy where C is shown below y (14) F1,2), (1.1)…

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Q: 2. Evaluate dy/dx for y= x In x 1+inx

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Q: Given tanh(x)+ tanh (y) = 1, show that, dy 1- y? dx 1- x2

A: We can find the required answer as below

Q: Find dy/du, du/dx, and dy/dx when y and u are defined as follows. and u = Vx + 3 V = - dy du du dx 3…

A: Trigonometric identities: 1.d/dx(xn)=nxn-1 2.d/dx(constant)=0 3.d/dx(root x)=1/2root x And given y…

Q: when y and u are defined as follows. y = 3u2 + 7   and   u = x2 + 9

A: Here I am attaching image so that you understand each and every step.

Q: dy 13. y(1) = e de ar(In y - Inr + 1)'

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Q: Use an appropriate technique to evaluate the following: 1 dx dy (1+x² + y²)²

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Q: In(3) In(3) dx dy y/2

A: on solving this we get

Q: er dy %3D sec da

A: The given differential equation is exdydx=sec y and the initial condition is y0=1. Solve the given…

Q: Given that y = ln |2² – 6 , dy 6, find dx In |x %3D

A: Differentiation is the process of determining the derivative of the function The given function is…

Q: S 6 ttan t dt = %3D dx Jx

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Q: If y = tanu, u =v--, and v= In x, dy at x= e? what is the value of dx

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Q: If we have to check the DE (5-8y+4xy)dx = (x+2)²dy for Exact then My

A: M dx + N dy =0