dy If x = t+sin t and y =1+cost, then find at t = dx O a.-2 O b. 2 O C-1 O d.0

Q: dy If dt = y cos(t) and y = 3 when t 0, then y= || sin t + 3 O esint + 3 O sint + 3et O 3esin t

A: The solution is given below in the next step:

Q: If x= sint and y = cost then 2 dx dy dt dt O 2 O -1 O 1 O O O None of these

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Q: Sclve th initial valu e probi dy + 2 . 3. dx3 dx? Y'c0) = 8 y"(0) = -4

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Q: If u = x+ 1 t = vu y = t? then, = 0 dy dx dy 2. = x dx dy 3. = 1 dx dy dx 1. 4.

A: (3) We have to find out dydx

Q: b) Given y= ae¯* sin(x+b) where a and b are constants. Show that d²y -2x dx +5y=0 dx

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Q: t+1 dy If x = and y = t2 - 2t +3, then find t-1 dx

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Q: Find the value of dy/dx at the point defined by the given value of t. x 5 sin t, y = 5 cos t, t= O…

A: Given, x =5sint  y =5cost We have to find the value of d2ydx2 at t = 3π4

Q: dy Given: y= tan x Find dt dx when x =- m and dt = 2 m/s 3

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Q: dy 2. If = y cos t and y = 3 when t = 0, then y = dt A. esint + 3 В. Зesint C. sin t + 3 D. sin t +…

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Q: Given a = 2 cost + 17 and y = 3 sin? t dx dt dy dt dy dx

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Q: Get z = f (x,y), x= e° cos t, y = es sin t Show that it's + ) - 2 2 =e 2s + əx. əs

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Q: dy given that: dx (a) Find 3yx + sin(2y – 4) = /(2y)

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Q: dy 28. (i) Find , where a) y= In b) x+y+ cosxy = 0 dy (ii) Given that x= e'cost and y=e'sint, find 2…

A: As per the guidelines we can solve the first three subparts or first one question. If you want more…

Q: Given y=squarerootx.  Find dx/dt when y=8 and dy/dt=1.75

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Q: Let w = 4e" dx /A dy + aeª dx ^ dz and n = 7e*Y dx + 8e² dy + eY dz, where a E R. Find the value of…

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Q: d?y What is the degree of the DE dy 3 dz 2 dx A 3 2 1/2

A: Degree: the degree of the differential equation is defined as the exponent of the highest order…

Q: d'y If xy + y' = 1, find the value of at 2 dx (0,1). %3D

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Q: If y = xcosx, what is dy if x = and dx = 0.2 ? 0-1/2 0-20 05/0 O EN T 10

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Q: Find  dy dx at the value of the parameter. x =    t,  y = 2t + 8,  t = 16

A: See attached file for a step by step explanation.

Q: Given z = 2 cost +3 and y= 3 sin? t dx dt dy dt dy dx

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Q: dy 18. Given y = 5t ( 3 - t), t = In p and p = e*. Find and simplify %3D dx

A: Given: y=5t3-t, t=lnp, p=ex   As we know from the chain rule; dydx=dydt·dtdp·dpdx    .....(1)   The…

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: 4. Find . d?y of the functions x = 1+ cost and y = 1– sin t. dx2

A: Differentiating given parametric equationswith respect to t,x=1+costdxdt=-sint…

Q: 2 Given z = 2 cost + 30 and y= 5 sin t dt dy dt dy dx %3D %3D

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Q: dz The sides of the rectangle below increase in such that dt 1 and a way dx dy 3. At the instant…

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Q: dy Find given that dt dx x² + y? = 2x + 4y, x= 3 y = 1, and 7 dt dy i dt II

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Q: dy Find dx at the point ( x, y ) = (1 , 0) If e *y = e * In(x²) + y² + 1 %3D

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Q: dy If x = t – sin t and y =1- cost, then find at t = %3D dx a. -2 b. 0 С. 1 d. 2

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Q: dy dx Find at the point (1, 1) on the curve: - 3x + 2y? + y +x – 7 = 0 dy dr 1 dy dr 7 dy dz dy 7.…

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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: Given x = 2 cost + 35 and y = 8 sin? t dx dt dy dt dy dæ || ||

A: Given equation is, x=2cost+35y=8sin2t

Q: dy If y = (In x) (sin x), then dx

A: y=ln x(sin x) To find dydx

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

A: It is simple differentiation.

Q: Q1-If x= cot-1 VE, y = find dy d2y dx' dx² at t = 2. t+1

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Q: (2)S, dx where c = constant let c-x = e-x Inc %3D

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Q: dy 3. given, y = sin[2tan-V then find 1+ dx

A: Given function is y=sin2tan-11-x1+x

Q: if y=u, u=v -1/2 and v=lnx, what is the value of dy/dx at x=e

A: Calculate the value of dy/dx and then put x=e .

Q: t+1 If x = and y = t2 - 2t + 3, then find t- 1 dy dx

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Q: dy a. Assuming y is a function of x, find dx for Rx sec(y) – 3y sin(xy) = eRxy. %3D

A: To find dy/dx

Q: Given x = 2 cost +33 and y=8 sin t |3D da dt dy dt dy dx

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Q: dy If y=t+t and x= 5t+7 then at x = 17 is: dx

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Q: 1. Given xy = sin x , show that d'y 2 dy +=+y = 0. dxx dx

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Q: If x = 5t +4 and y = 3t-7 , then find dy at t = 2. dx а. 1 O b. 2

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Q: dy given that: dx (a) Find 3y²a x+ sin(2y – 4) = / (2y)

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Q: Given x = 61 sin t + 36 and y = 3721 cost – 29 - dx (i) dt dy (ii) dt dy (iii) dx

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Q: Let @ = 7e* dx ^ dy + ae³ dx ^ dz and n = 7e*y dx + 14e* dy+ e³ dz, where a E R. Find the value of a…

A: Given: 2-form, ω=7exdx∧dy+αeydx∧dz. 1-form, η=7exydx+14exdy+eydz.  where α∈ℝ. To find: The value…