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

Q: dy = 4. Find dt dx when x = 5. dt Suppose that a point is moving along the path xy = 5 so that

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Q: Suppose h(x) = cos(tť² )dt Calculate h' (x).

A: Given: hx=∫0x3cosπt2dt.

Q: x2y3-y=x+x2 find dy/dt

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Q: cos (2t + ) dt e21–3 %3D 4 -3 4 64e3 7.

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Q: Solve the problem. Suppose that " g(t) dt = 4. Find S* ste) dx and *- gt) dt . -1 1; 4 0; 4 O 1; -4…

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Q: Find g'(x) if g(x) = t² cos 6t dt %3D 2

A: We can apply fundamental theorem of calculus here.  The second fundamental theorem of calculus…

Q: find dy/dt. y = ecos2(πt-1)

A: We use the chain rule to find the derivative

Q: dy Compute dt t=to .2 x+6 y = X-6 X = 4 to = 3. dy dt t=to (Simplify your answer.)

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Q: ds if s = In [t*(t² – 1)]| dt 20. Find

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Q: 2. (e2y – y cos xy)dx + (2xe2y - x cos xy + 2y)dy = 0

A: Exact differential equation

Q: (t + z cos(t)) dt + (sin(t) – 3z² + 5) dz = 0

A: Let's find.

Q: If y = x3 – 2x2 + 3 and x = t² + 2 find dy at t=2. dt %3D

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Q: H(x) = . (1+ sin t) dt Jx2-3x

A: Use the fundamental theorem to determine H'(x). Find the derivative at x=1.…

Q: Integrate (a) S2(* dt (b) S(x+1)³ dx (c) cos(-x)(x²)dx

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

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Q: 1. Suppose f(x) = S*,t cos (e) dt. Find f'(x) COS 1+t2

A: We have to find f'x for the function: fx=∫-7xtcos11+t2dt This type of derivatives would be solved by…

Q: - Find dy at x = -1 if y=u³ +5u-4 and u = x² + x. dx

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Q: dy Compute dt t=to X+3 =x-3 x= 4 to = 3. %3D dy dt t=to (Simplify your answer.)

A: We have to find derivative

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

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

A: x=2cost22

Q: if x² + y² =t -- and x* + y* = t dy prove dx 1

A: Given, if  x2+y2=t-1t and  x4+y4=t2+1t2 To prove that  dydx=1x3y

Q: find dy>dt.…

A: Given function, y=ecos2pt−1

Q: ify+. 1 -dt = xy rsecx Q3.a) Find if y + S V sint+1

A: According to our answering guideline we can answer only first question if multiple questions are…

Q: dy Q1) Compute for y(x) = sec (2x) + 2x-1 and dt x(t) = 4cos(t2) at t-1 %3D

A: From the given problem:   yx=sec32x+2x-1xt=4cost2   Now applying the chain rule:   dydt=dydx.dxdt…

Q: b) f(x) = In(1 – 3x) %3D c) f(x) = cos(t³) dt

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Q: If F (x) = (t2) dt , then F' (4) = cos 0,

A: DUIS rule is used

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: Find F′(x).

A: Given- Fx=∫02xcost4 dt To find- F'x Concept Used- The Leibnitz's theorem as  ddx∫gxhxft…

Q: S(1- cos )´sin ź dt, u = 1 – cos 4. U = V5x+8' dx ,u 5x + 8

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Q: Q3) Compute for y(x) = cos'(4vT)+ 5x and x(t) = 4 at t=1

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Q: dx + 2x = dt dy + 10 cos t, dt ay + 2y = 4e-2t – dt 业 da if x = dt rstem

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Q: s^2ds+2t(s+1)dt=0; s=0, t=1

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Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: 4) (2x + y cos xy) dx t x cOs xy dy - o cOs xy) dx t X COS Xy dy COS

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Q: Find dy/dt. 13) y - cos (πt - 19) 14) y = 4t(5t + 2)4

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Q: Find dy at x = -1 if y = u’ +5u – 4 and u = x² +x . dx

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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: 3. (sın 2y - 2x cos 2y) dx +( 2x cos 2y + 2xsın 2y)dy=Dd X = 2, Y = TT when

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Q: - (f* (t² + 1)¹⁰0 dt)" dt - Some ₁ tanx 1 + t2 d. y = e. y =

A: According to Leibniz integral rule : ddx∫a(x)b(x) f(x)dx=fbxddxbx-faxddxax

Q: dx = x(x 1)(x + 1) dt has a solution that is

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Q: Find dy if y = In* +1 7 -t dy dt

A: Derivative is below

Q: 1. Determine the general solution of (x 3y )dx – x dy = U

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Q: Find dy/dt at t=9 given that y= (u+2)/(u-1), u= (3s-7)2 and s= √t

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Q: (sın 2y - 2x cos 2y) dx +( 2x coS 2y + 2xsın 2y)dy=d when x= 2, Y = T 3. COS %3D

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Q: 3 * (dx)/(dt) + (dy)/(dt) + 2x = 1, (dx)/(dt) + 4 * (dy)/(dt) + 3y = 0  Given x = 3 y = 0 when t =…

A: As per the question we are given the following system of differential equations : 3x'(t) + y'(t) +…

Q: d If g (x) =-=-^[e'- In(2t+1)]dt, find g''(x) . dx -2 A ex-In(2x+1) 4 B et + (2x + 1)2 4 (2x+1)2² 2…

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Q: Find the particular solution if dy/dt=sin(t) and y(2)=2.

A: Topic:- application of integration

Q: dy Compute dt t=to X+3 y=x-3x=7 to = 3. dy dt t=to (Simplify your answer.)

A: Solution: The objective is to find dy/dt at t=3

Q: d If g(x) == _S^*[e' − In(2t+1)]dt, find g ''(x) . - dx -2 2 A (2x + 1)² 4 B (2x + 1)² 4 (2x+1)2…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.