If y = #(x – 1)7 then y' at æ = 2 Is equal to Select one: а. —5 b. 5 c. d.

Q: Given that y =5u'+4u and x 1 hence find dy dx

A: Differentiation problem

Q: - Find dy /dx for the given function y? cos fy)=2x +2y

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Q: Solve the following DE using variation of parameters (D – 1) y = e" + 1 -

A: Let's find.

Q: dy dx\, Given that x = t e and y = 1² e“ +1¸ Find = - 1

A: We have to find derivative at that point

Q: Given a6x CosT+Sy - .3x. -Siny+ 10x-e -*, defermine (1) T'=S(T) ax T'-

A: Given:T"=6x2y3-cosx+5y2-siny+10x2-e-3xTo determine:i  T'=∫T"dxii  T'=∫T"dy

Q: Given a level suface 4x2y2 + 5xy = 4 with y = y(x). Find! dy at the point (3, 2). Give your answer…

A: A detailed solution is given below

Q: 1 In (a² + y? + 1) dædy -VI-y? |

A: I use polar conversion method to solve this double integral

Q: Given that y'= 3y - 100t and y(0) = 10, estimate y(1) using delta t= 0.01.

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Q: Given ey = x + y. Show that x +y (x + y – 1)3 d?y dx?

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Q: y to solve the following linear differe ] dy

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Q: Find the DE by eliminating the arbitrary constant  y = A+ bex

A: Given equation  y=A+be^x Where A & b are arbitrary constant.

Q: If z = 5x2 + y2 and (x, y) changes from (1, 2) to (0.95, 2.1), compare the values of Δz and dz.…

A: We have to compare the values of Δz and dz.

Q: -30t si'n got dt

A: We know, ∫eatsinbtdt=eata2+b2[asinbt-bcosbt]+C, C is a constant

Q: dy of the following implicit functions. dx Find ху - Зу 10x 3.

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Q: dy Find dz If ze" + (Inz)y + y? = 3

A: Find dydx if xex+ (ln x)y +y2 =3 We will differentiate terms and then sum them up. So, ddx(xex) =…

Q: Find the antiderivative of the given derivative. ds = 5t(212 – 1)3 dt

A: Solution:-  given that  dsdt=5t(2t2-1)3 now  using identity (a-b)3=a3-b3-3ab(a-b)

Q: For x-Arccos(31) y=Arctan(6t) find y when x=D0 0-1 0-2

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Q: dy 5. If y = e+1 sin(1 – a2), then Find dx

A: We need to find the derivative of y=e3x+1sin1-x2 We will use the product rule to find the derivative…

Q: Find the antiderivative of the given derivative. ds = 9t(2t? - 7)3 dt S =

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Q: If 3x2 +2xy +y² = 2, then the value of dy at x=1 is dx

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Q: For ey – In x=y2, find the value of so that & (y' – y') = 1 at y =0- O e e

A: we have to find

Q: dy 91. t In t for y = el

A:

Q: Find the following derivatives. where z= e 9x + 4y x = 3st, and y = 2s + 4t Zs and Zt,

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Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. y3+x5y4=−1

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Q: Find the devivatives of the following equation b Y= ln (x,4)-x fori CH/2)

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Q: If y = 1+sin t ,x = cost at t = dy Find- dt by using Chain Rule, then choose the correct answer: a)…

A: Given curve is  y=1+sint  ,x=cost

Q: If y = 1+ sin t ,x = cost at t == 2 Find- dt by using Chain Rule, then choose the correct answer:

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Q: Find the G.S.of the DE. (ytu dy=D0

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Q: If xy + ey = e, find the value of y′′ at the point where x = 0.

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Q: If xy + ey = e, find the value of yn at the point where x = 0.

A: xy + ey = eWhen x = 0,  ey = e = e1Hence, y = 1

Q: If z = x² – xy + 2y² and (x, y) changes from (3, –1) to (3.03, –1.05), compare the values of Az and…

A: given: z=x2-xy+2y2 and (x,y) changes from (3,-1) to (3.03,-1.05). we have to compare the values of…

Q: dy dz 4 + Va Find for y =

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Q: If y = 1+ sin t ,x = cost at t = Findy by using Chain Rule, then choose the correct answer: dt

A: Given that: y=1+sintx=cost

Q: 3. a) Use the trapezium rule with five ordinates to find an approximate value for S dx, giving your…

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Q: Find the solution of dy X. +y.Inx y.lny dx Show all your calculations.

A: Given equation is as below :

Q: if y=tan u, u=v -1/v and v=ln x, what is the value of dy/dx at x=e

A: We have to find dy/dx .

Q: (b) Solve the following initial vahue problem by separation of variable = 2x at x = 0, y=-2 dx

A: We will solve the problem

Q: хуз dx + e** ,3 dy = 0.

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Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. −4x2 −3x−1=y2 −y

A: The given function is,

Q: If z = 9x + y² and (x, y) changes from (1, 3) to (0.95, 3.1), compare the values of Az and dz.…

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Q: are

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Q: d’y If y= cos 2x, then at dx? x = 0

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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 the antiderivative of the given derivative. ds 14(4? – 1)3 dt S =

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Q: Find the value(s) of @ for which y = cos ot satisfies d'y + 16y = 0. di? Enter your answers in…

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Q: Differentiate e w repect to X. expression (x2+y)" (use D fur dy)

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Q: Find L ft ={fe',01 el-s -1 b. 1-s e -1 et -1 а. 1-s C. 1+s e- -1 d. 1-s

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Q: Why is e^x selected as u and not e^2x (to get du /2 = e^x dx in the problem attached?

A: Consider the integral  ∫e2xe2x+3ex+2dx

Q: If x2 + y2 = 100 and dy/dt = 4, find dx/dt when y = 6. (Enter your answers as a comma-separated…

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Q: Find the antiderivative of the given derivative. ds = 14t(5t2 – 1)3 dt S=

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