dy Find dx t2 + 4 y = 3 t X = a) b) y= t2 – 2t, x = In 2 t c) y = 4 – 4t – 4t2, x = 2t

Q: dy If y = (t + 6t + 4) (3t2 + 4), find dt dy %3D dt

A: it is required to find the derivative.

Q: Prove that when y = e 2 Sin 2.x, then 4- d y dy +17y=0 +4. dx? dx

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Q: fo axy dx + 2xy dy, where Cis the rectangle bounded by x = -1.x = 1, y = 1, and y = 5. 6xy dx + 2xy…

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Q: Compute Scy dx + xy dy if C goes from (0,0) to (1,2) along the line parameterized as x = t, y = 2t.

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Q: Which of (a)–(c) is not equal to s(x, y, z) dz dy dx? IIT ra, y. 2) dy dx dz (a) 13 III ra,y. z) dz…

A: Explanation: Given that,  ∫01∫34∫67f(x,y,z)dzdydx   Concept Used: In ∫ba∫cd∫efg(x,y,z)dxdydzlimit…

Q: dy Find da if y = In(xiV1+ z° dy %3D dx

A: Recall: d(u.v)dx= u dvdx+dudx v d(xn)dx= n xn-1 d(ln x)dx=1x

Q: dy Let y = f(x) such that In(x – y) = 2x – y + e². Find dx

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Q: dy If x = t - t3 and y = t2 - t, the value of at t = 2 is %3D %3D dx

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Q: d²y dy dt + 81y = 0, y(0) = 9, y' (0) = 3 + 18- %3D %3D dt?

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Q: dy If y = (t + 2t + 8) (6t² + 6), find %3D dt dy dt

A: The given question can be solved as shown in step2.

Q: Find dy/dæ in terms of æ and y if æ°y – x – 2y – 1 = 0. dy dx

A: We have to find dydx in terms of x and y if x3y-x-2y-1=0.

Q: Integrate by Substitution. 1. dx where u = Vx+2 2Vx+2

A: By using substitution method, we calculate the given integral.

Q: Show that S f(x,y) dy dx = , f(x,y) dx'dy. %3D

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Q: f (x, y, 2) = In (x² + y? + ²) ve df x = cost, y = sint, z = tise dt It%=D1

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Q: u + c. Evaluate So (2x- y)3e dx dy with y = v, x= u-

A: To evaluate ∫02∫y22+y22x−y3eydxdy with y=v, x=u+v2.

Q: If x = 2t2 +t+1 and y=8t3+3t? + 2 then dy at t = 1 is dx

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

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Q: dy is : If x- y 0, then %3D dx

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Evaluate the line integral / (2x + 4y)dx + (2x – 9y)dy along the curve C : x = 4 cos t, y = 8 sin t…

A: Solution is given below:

Q: Find aff dy dx² for f(x, y) = exy

A: I have done solution in detail....step by step....go through the solution

Q: Hiws slove du 4 dt %3D dx2 u(6,t) = L (8,t)=0 U(x, a) =0 : =4X-()x²

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Q: (a) Let I = dx. Show that I² = dx dy. R2

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

Q: dy Find given that dt dx x + y = 2x + 4y, x= 3 y = 1, and %3D = 6 dt dy %3D dt

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Q: Find of / dx and of / dy. f(x,y) = e(x+ y + 9) of / dx = df / dy =

A: Let f be a function of x and y. The expression ∂f∂x implies that partial derivative of f with…

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: Solve the DE using homogenous equations: Let: x = vy dx = vdy+ydv xy dx - (x2+3y2) dy = 0

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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: 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: dy Find , if dx y = 3u – 2 and u = 2x² - 4. dy Preview dx

A: Topic = Derivative

Q: Show that if y = cosx/x , then d^2y/dx^2 + 2dy/dx+ y = 0

A: y=cosxx Differentiating with respect to x, we get dydx=dcosxdx·x-dxdx·cosxx2…

Q: Show that d/dz(z^2 z ̅) does not exist anywhere.

A: Here we show that ddzz2z does not exist anywhere.

Q: The value of the line integral S(2xy² dx + 2x?ydy + dz) along a path joining the origin and the…

A: To find the value of line integral  ∫c(2xy2dx+2x2ydy+dz)along the path joining origin and point…

Q: || (z, y) dy de = f(r,y) dx dy 0. Jo Jo O Tryc

A: Solution: The objective is to select the correct option

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

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Q: Evaluate dy/dx when t = 7 such that: y = 2z^2 - 3z + 5 x = 4t^3 + t t = z^2 + z + 1

A: Given                y=2z2-3z+5           (1)    x=4t3+t                   (2)    t=z2+z+1…

Q: If y =Aex +Be™ d'y -(m+n) dy. Show that + mny = 0 dx

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Q: Solve for if y- Ina 2- y?. da MCQ3.pdf dy 2y +1 dx dy 2y +1 dx dy dæ -(2y+1)x 1 dy (2y+ 1)a TERIRS…

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Q: 2 In(t) and y=4 t2 then find %3D %3D dy dx d'y dx2

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Q: Evaluate the line integral / (3x + 7y)dx + (2x – 3y)dy along the curve C: x = 6 cos t, y 12 sin t…

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Q: JS xy dA R: rectangle with vertices (0, 0), (0, 3), (5, 3), (5,0) 166xx 16 xy dx dy = xy dy dx =

A: The solution is given as

Q: (2^)u sec (VTt) 2V7t (a) y= tan dy: dt 5- v2 (b) y = 5 + v2 dy = -5- 2iv 5 -V-5-2iv5 %3D Need Help?…

A: Both the parts are given below.

Q: dy If y = (t + 5t + 6) (2t² + 4), find dt dy %3D dt Submit Question

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Q: Find dx/dt. Uince x² + y^ = 225, then. 2x dx dt 2y.dy 24- ニ

A: Given that x2+y2=225 we have to find the value of dxdt.

Q: d?y e. dt? dy + 4y = 8t – 10, y(0) = 1, y'(0) = 75 %3D dt 2

A: As you asking multiple questions so I answered only first

Q: dy (a) Find if y = (In x)=². dx

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

Q: By algebraic substitution, the integral dx dx is converted to: 4+Vx dy y+4 2 dy y+4 ydy y+4 2ydy y+4

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Q: y = x*, d'y 1 dy dx y dx, Prove that Y = 0. X

A: First we find out dy/dx then d2y/dx2. And put the values of dy/dx and d2y/dx2 in given condition.

Q: dy find 3 - x x - 2 1) If y = t + 2t , t = %3D %3D dx

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…