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

Q: Let y tan(4x + 4). Find the differential dy when x = 1 and da 0.4 Find the differential dy when a =…

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Q: S cos ædx from a = 0 to b = %3D %3D 3.

A: Substitution is done.

Q: 14. Determine dy/dx if y is a function of x defined implicitly by sin(x? + 2y)

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Q: dw Find the value of- dt at the point (1, In 2 ,0) on the curve x = cos t ,y= sin t, 0 <t< 2n where…

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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: dy at t= T is dx If x=t+sin 2t , y = 3t – cos 2t, then O a. -1 O b. 1 O C. -2 O d. 2

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Q: ecsch(ry) + Tr° -cos(0)

A: Let's find.

Q: dy dt 1 if 4y°t + t°y = 5 and dx Find dx cos t dy %3D dx

A: Given; 4y3t + t3y = 5 and dt/dx = 1/cost.

Q: dy Find the derivatives dx of the following functions csin x Vt2 + 1 dt 2

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

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Q: Find dy/dt if y = tan^−1 (1 /√t)

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Q: dy dt 1 if 5y°t + t°y = 3 and dx Find dx cos t dy dx

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Q: find dy/dt. y = (t-3/4 sin t)4/3

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Q: If the PSD of X(t) is S„(@). Find the PSD of dX(t) dt

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Q: dy b) Find If tan2²(2y) – S cost dt = 4 – x2 - dx

A: We find the dy/dx by Leibniz rule.

Q: Find dy/dx in terms of t if x = te', y = 4t + 4e* dy/dx =

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Q: dy if 4y°t + t°y = 5 and dx dt 1 Find dx cos t dy dx

A: We have to find out

Q: dy dt 1 if 2y°t + t°y = 3 and dx Find dx cos t dy dx

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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: dw = t³ and y = 7. Find dt Let w = cos(8x - 10y), where x =

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Q: Let y = tan(5x + 3). Find the differential dy when æ = 2 and dæ = 0.3 Preview Find the differential…

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Q: dy Find dx S cos (P) at y = COS dy dx II

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Q: determine dy/dx if xy = ecsch(x)+πcos(0)

A: Given, xy = ecsch(x)+πcos(0)

Q: Let y = tan(3r + 4). Find the differential dy when T = 4 and da 0.4 Find the differential dy when x…

A: Given: Differentiate the above expression of 'y' with respect to 'x'.

Q: dy 4) Find dx when y² – x² + cos(x + y) = 0

A: As we know that the derivative of : ddx(xn)=nxn-1 ddx(cos(x))=-sin(x) ddx(f(g(x)))=f'(g(x))g'(x)

Q: Find dy/dt. y= cos ~ 10t + 11)

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Q: dF find F (x) = J- dx but -x cos(tx) dt t

A: A

Q: dy Find for y = cos (8at + 1). dt dy dt

A: We have to find out dy/dt for given y

Q: Find dy/dx in terms of t if x = te', y = -5t – 5e dy/dx = [

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Q: dx y of y = cos 1 (In (xy)) Find %3D CoS dy

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Q: Q5.a) Find if sec?y = x? + t² dt Jsiny dx dy pcotx b) Find if tan²y = x² + VE² +1 dt dx

A: Solution:a) Given :sec2y=x2+∫sinxcosyt2 dt

Q: Find dx/dt Xt2 = x – cos1 (t)?

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Q: A ) Find ſ cos 5t dt dy B) If y = x² +; , x= 2t -5 then find dt

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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: d 2x Le arctan t dt dx

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

A: topic - derivatives and integration

Q: dy Find dx if y = a (sin (1))". dy

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Q: x=24 sin t + 6 and y=24 cos t+39 Find: 1)dx/dt 2)dy/dt 3)dy/dx

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Q: I. Find dy/dx in the following: 6. Y=sec² Inx

A: We are given: y=sec-1 lnx The derivative can be found as follows:

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

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Q: Find dy/dx: 1. у%3D Jo = San* sec? t dt

A: A detailed solution is given below

Q: dy Find dt y = tan ( sin (4t - 3))

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Q: Find dy/dx in terms of x and y if cos² (4y) + sin“(4y) = y + 8. %3D

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Q: Find dy/dx √(1+cos^2y) =xy

A: Given  (1+cos2y) = xywe find dydx

Q: dw Find dx where w = cosz- cos 4x cos'4y + sin 4x sin 4y and z= 4x+ 4y. dw 口

A: lfirst put value of z and then expand cos term Now we get Zero whose derivative is zero

Q: dy 1 cos t + 1 dt 2 || ||

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Q: Ql find dy 2メ for y= cos ( Inx + e %3D dx

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