. If y = tan( sin t (. cos t-1 1 dy %3D show that dt 2

Q: c) dx E (sin cos) dt

A: We find ddx ∫xπ/2   sint2   cost3 dt

Q: 7. Find dy dx (a) y = (x* + 5x) cos 5x, %3D

A:

Q: 7 sin°(e) cos"(t) dt

A: To evaluate the given definite integral

Q: 4X dy 2siny ?) S dy sinzx e 3) S sin? dx

A:

Q: You tart muesting at t=0 y co) =0

A:

Q: H.wl: Find L{e-3t St. sin 2t.dt p1 p2

A:

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

A:

Q: If Xy +y.1 find the value of dy dx 2 5- at the point Co,-1)

A:

Q: I. Find dy/dx of the following: COS X √4-3x² 7. y In- 8. y In, 6. y = In(In x) 9. y + ln xy = 1

A:

Q: dz evaluated at dt If z=tan In with x=sec t and y=eª. Then the value of t= 0 is equal to ...…

A: Chain Rule Let us consider the function z=f(x,y) where, x=g(t) and y=h(t) Differentiate the function…

Q: Solve the given DE: dy ex – 2x cos y ey – x² sin y' - dx

A:

Q: Given x 2 cos t + 2 and y 4 sin? t dx dt dy dt dy dx ||

A: First we will differentiate the given equation with respect to t

Q: Solve the following DE: [2x+ ycos(xy)] dx+ x cos(xy) dy = 0

A:

Q: If y = In(x² + 5) + sinx function then ay at x = 0 is ? dx 11 10 1 10 O 1 O 5

A: Given, y=lnx2+5+sinx  We have to find  dydx at  x =0

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

A:

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

A: x=2cost22

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

A: Let's do derivative of given function.

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

A:

Q: If Y= e(sin x) dt apoint X = 2 then dy/dx

A:

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

A:

Q: FIND DY/DX OF THE FOLLOWING 6. y=sec'Inx

A:

Q: 1. Evaluate x + x? (y) dy dx. COS

A:

Q: Given a = 2 cos t + 3 and y = 3 sin? t dx dt dy %3D dt dy da

A: From the given problem:   x=2cost+3  &  y=3sin2t   So, a)…

Q: dy 2 5. Find if y = sin (27t)+tan-(2Tt) dt

A:

Q: If y = x* cos' x-e* In( 7x +1) , then find dy at x=0. dx 3

A:

Q: The integrating factor of the LDE y =x-2ycotx is A cos?x B sin3x © sec?x D csc?x

A:

Q: d. t sin 2 dt COS dx 3

A:

Q: d²y +9 = cos?t+ sin? t + cosh t + sinh t +3 sint -3t dt %3D dt2

A:

Q: The integrating factor of the equation sec? y + xtany= x° is: dy de In|sina| O None of these…

A: We have to find I.F

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

A:

Q: 5. Evaluate r'sin(y³) dy dx

A:

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

A:

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

A:

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

A: We use parametric differentiation

Q: (a) Find dr dy given that x²y + sin xy = 0.

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

Q: -T/6 T So Soo S xy sin(yz) dx dz dy.

A:

Q: Solve the following problem dw dw + x dt 1, -00 0, %3D dx with w(x, 0) = f(x).

A:

Q: (dr Ifr=a cos ti +a sin tį+ at tan 0 k, find dt dr at t = 0. dr?

A:

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

A:

Q: 5. e tan y dx + (1-e) sec? y dy = 0. %3D

A:

Q: I. Find dy/dx in the following: 1. Y= sin In(x + 1)

A: To find the derivative of given function.

Q: dy If x = t? cos? 3t y = 3 sin 3t find dx

A:

Q: Given x = 2 cos t + 24 and y = 6 sin? t dx dt dy dt dy dx || || ||

A: Let x = 2 cos t + 24 and y = 6sin2(t) Differentiate x with respect to t…

Q: 1.) dx = t (1 + t2) sec?x dt ans: 2x + sin2x = (1+ t?)² + c

A: Since you have posted multiple questions in this question i can do first question as per our company…

Q: S 6 ttan t dt = %3D dx Jx

A:

Q: d. a) dt [8 sin 1 2t] = d. b) |7 cos s 1 5 dx d. 3u] = -1 c) 10 sec du

A:

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

A: To find the following