Given x = 2 cos t + 1 and y = 8 sin? t %3D dx dt dy dt ||

Q: If z = xy + 3xy', where x = sin 2t and y = cos t, find dz/dt when t = 0.

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Q: find dy>dt.…

A: Find dy>dt dydt>1 dcostdt=-sint

Q: If the given linear DE is (y – cos² x)dx + cosxdy = 0, what is the integrating factor? Select the…

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Q: dy dt 1 if 7y't + t°y = 5 and dx Find dx Cos t dy

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Q: dx/dt + 4x = cos(2t), x(0) = -1 Find x(t)

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Q: The integrating factor of the linear DE dy - 8y = 5 cos x, dx is the function µ(x) = e-8z Select…

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Q: Find d2x/dt? as a function of x if d 6x sin x. dt? ||

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Q: Find dw/ dt at t = 0 if w = sin (xy + p), x = et, and y = ln (t + 1).

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Q: If y= sin f dt, then dy is dx 2x sin x sin x 2 VX sinx 2x sinx

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Q: Find the value of dy/ dt at t = 0 if y = 3 sin 2x and x = t2 +π.

A: Given : y=3sin2x, x=t2+π To find : dydt We can write dydt as, dydt=dydx×dxdt                    1…

Q: 16. t 31²y = cos t, y(T) = 0 dt

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Q: If z = cos x - e¹, x = 1² + 1 and y = 5 + ln t, then equals: dz dt

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Q: Find dx/dt: x = 2[cos (t/2)]^2

A: x=2cost22

Q: x2 dy Find - for y = x dx -for y =x cos t?dt. sť dt. 2

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Q: dy dt 1 Find if 4y°t + t°y = 2 and dx dx cos t dy dx

A: To find dydx here we need to use both chain rule and product rule of differentiation.

Q: dw "(1),y = sin (1),-: 2) w=+ x= cos at =3 Ans. -1 dt

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Q: If y = In(2x+3) , then find dy at x = 0. dx

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Q: Given x = 2 cos t + 8 and y= 4 sint dx (i) dt dy (ii) dt dy (iii) dx ||

A: Givenx=2cost+8y=4sin2t

Q: . The exact differential d(xy)= xdy + ydx, what is the d( = 4x²y'dy+2xy*dx.

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Q: Find the differential dy of the given function. y = csc 5x dy dx

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Q: d'y 10ay+25y = 0. dx? 1. Find the general solution for dx

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Q: Given x = 2 cos t + 24 and y = 2 sin t dx (i) dt dy (ii) dt %3| dy (ii) dx || ||

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Q: (a) Find the differential dy. y = cos(x)

A: Differentiate the given function with respect to 'x' and find 'dy'.

Q: Find dw/dt at t=0 for the function w=sin(x),cos(y),ln(z). Where x=-7t^2+9t+pi/2, y=t,z=e^-6t

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Q: dz Find dt if z = x²y – sin y, x = vt? +1 and y = e -

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Q: If the given linear DE is (y – cos² x)dx + cosxdy = 0, what is the integrating factor? |

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = (x+1)/(3x-5)   dy=

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Q: dy 1; find dt dx at x =- dt Related Rates: Given y = cOs x + sin and 4

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Q: 87. Find the value of dy/dt at t = 0 if y = 3 sin 2x and x = t+pai

A: Given, y=3sin2x,  x=t+π y=3sin2t+2π we know, sinA+B=sinAcosB+cosAsinB sin2t+2π=sin2tcos2π+0=sin2t…

Q: Find the differential dy of the given function. dy sec x x² +9

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Q: d’y Find the particular integral solution of dx dy =x+3 cosx+e-*. dx

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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: dx 2а — У dt fip dt x + 2 cos(t)

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Q: Find dx 2n S sin (P) at (?)dt y=

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Q: Find dw/ dt at t = 0 if w = sin (xy + p), x = et, ln (t + 1).

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = -5x – (sin(x))² dy =

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Q: dw (C): If w = tan x and x = 4t³ + t ; Find ? dt dy

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Q: Given z = sin(1 - 2). x = 2 – ts and y = 2t – s - then calculate when t = -1 and s = -1. dt

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Q: dW Find at t=0, if dt .3, W = x*y+ zxy whe x = sin2t, y = cos ?

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Q: Given x = 2 cos t + 48 and y = 8 sin? t dx dt dy dt dy dx || || ||

A: We use parametric differentiation

Q: dy Find dx' 1/2 J cos (?) dt y =

A: topic - derivatives and integration

Q: What is the characteristic equation for dy 2. dt d²y y +2+e' sin 3t dt 2

A: Characteristic equation for the given differential equation:

Q: Find the differential dy of the given function. Y=x+1/3x-2 Dy=?

A: Given, y=x+13x-2

Q: If x = 3 sin* t and y = 2 cos" t , then find dy at t = dx 4

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = arctan(x – 2) dy = ||

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 4x + (sin(x))² dy

A: The solution is given below

Q: If x^2+y^2=25 and dx/dt=6, find dy/dt when y is positive and (a) x=0: x=1 x=4

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Q: Given x = 2 cos t + 18 and y = 3 sin? t dx dt dy dt dy dx

A: To find the following

Q: 3 dy Find dx if y = cos vx + 4sin x – log 3(3x + 1)ž. إضافة ملف

A: We will solve the following

Q: dy dt 1 Find dx if 2y°t + t°y = 4 and d.x Cos t

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