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

Q: Given y = 3x2 and x = t2 - 1, find dy/dt for t = 1 %3D 1) 3 2) 6 3) 0 4) 12

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Q: If x2 + y2 = 100 and dy/dt = 8, find dx/dt when y = 6. (Enter your answers as a comma-separated…

A: Consider the given: x2+y2=100 Differentiate w.r.t. "t",…

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 dy/dt and d^2y/dt^2 for function aln(y)+b cos^2(ty)=2t^3 where a  and b are certain constants.

A: Derivative two times simultaneously and use the forma for derivative

Q: If t = x + ex, find d2x/dt2 given dx/dt = 1 / 1+ex.

A: dcdt=0 , where , 'c' is any constant. dexdt=ex .dxdt

Q: d Vi In(t)dt equals dx

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Q: find dy/dt. y = ecos2(πt-1)

A: We use the chain rule to find the derivative

Q: If x^2+y^2=36 and dx/dt=9, find dy/dt when y is positive and (a) x=0: dy/dt= (b) x=2: dy/dt=  (c)…

A: Given: x2+y2=36    -1⇒y2=36-x2⇒y=36-x2   -2dxdt=9   -3

Q: (a) Find dy/dt, given x = 1 and dx/dt = 8. dy/dt = (b) Find dx/dt, given x = 36 and dy/dt = 3. dx/dt…

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Q: If xy = 4 and = -5, then what is dt dy when x = 4 and y = 1? dt OA. 8 8. OB. C. 8 OD.

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

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Q: dy/dt= 2e-t/8, t is greater than or equal to 0

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

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Q: dy dæ 2 and dt at x = 3 if y = 3x? 4. Find dt

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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: If g (x): A d dx [e' — In(2t+1)]dt, find g''(x) - -2 4 (2x + 1)² 4 B (2x+1)² Ⓒe*-In(2x+1) 2 D (2x +…

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Q: if xy+x=12 and dx/dt=-3, then what is dy/dt when x=2 and y=5?

A: Given :xy +x = 12

Q: 06: b: dw (1) Find if dt w= w = tanx and x = 4t³ + t.

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Q: dy t² +3 21. Find 9 if y = In dt /1-t,

A: We need to find derivative of given function with respect to t

Q: y = tan (5t - 21 +1)

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Q: dy Find for y = /12+13t dt. dv

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Q: If L= x + y dx dt and dy =3 dt what is dL dt when x=5 and y=12 Provide your answer as a decimal,…

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Q: Suppose 4x + 9y² = 36, where x and y are functions of t. (a) If dy/dt =, find dx/dt when x = 2 and y…

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Q: Suppose you know that dy/dt = 7y and that y(0) = 4. Which of the following answers is closest to…

A: We have to solve the differential equation

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

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Q: 크(F(a+) e dt dx 19

A: We have to evaluate, ddxFx4=ddx∫10x4  e-t2 dt

Q: dy 4) 0 and y > 0 dt dy 5) > 0 when both t >0 and y < -t dt

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Q: Find the value of dr / dt at t = 0 if r = (θ2 + 7)1/3 and θ2t + θ = 1.

A: Consider the provided equation, r=θ2+713 and θ2t+θ=1 Find the value of drdt at t=0. Apply the chain…

Q: Find da d.t da dt at x = 4 if y = 4x² – 1 and > Next Question dy dt = - 5.

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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: S(t)e¬Jwnt dt_ 2 C =

A: In this question, we find the coefficient for the Fourier complex series cn=2T∫0Ts(t)e-jwntdt

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

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Q: t2 + 9 V8 - t dy if y = In dt Find dy dt

A: Given equation is y=lnt2+98-t. Compute the derivative with respect to t.…

Q: dy If y = (t + 6t + 5) (6t² + 6), find dt dy dt ||

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Q: E. Find , and in terms of dx dt' dt 1. x = t°- 1 2. x = 4t + 3 y = 3t – 2 y = 4 - t

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Q: dy Solve the ODE dt = ty(5-y) dy - t y(5– y) dt

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Q: If eSp e = p + t, compute dp/dt when p = t = 0. p'(0)

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Q: Assume y′means dy/dt. Solve y′′+ 3y′−7y= 0

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Q: dy Find given that dt x² + y² = 2x + 4y, x = 3 y = 1, and dy = | dt dx dt = 6

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

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Q: dy – 2ty = –31²e? dt - and the condition v(

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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: Can i get help step by step please

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Q: (b) If z = 9t²e 4t, find 4 dz dt

A: Given.

Q: dy Compute dt t=to y=x? - 6x, x = r? + 4, to = 0. dy dt t=to

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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.