a) If d'r = 3, when t = 0 we have dt? dx 0 and x=0, what is x as a function of dt t?

Q: 1. Suppose y = f(x) and that x is changing over time. How is dy/dt related to dx/dt?

A: Given that: y=f(x)

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

A: Given: hx=∫0x3cosπt2dt.

Q: Can i get help step by step please

A: Given,

Q: Example 64. Solve the simultaneous equations: dx -y3 e', dt dy +x = sin t, given x (0) = 1, y (0) =…

A: Given dxdt - y = et    --- (1)dydt+x = sin t   ---(2)with  x(0) = 1, y(0) = 0

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: The equation dx/dt = kx is both separable .4 and linear اخترأحد الخيارات

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Q: EVALUATE AND SOLVE THE LINEAR DE. d²x dx + 2,+ 5x = 8e¬ dt2 dt dx When t=0,x=0 dt 8 =

A: Given that: d2xdt2+2dxdt+5x=8e-t

Q: Given x= 2y? , evaluate dx dy at y = 1 and dt dt 3.

A:

Q: (a) x = 0: dy/dt (b) x = 2: dy/dt (c) z = 3: dy/dt

A: Given that x2+y2=25, and dxdt=6 we have to find dydt when y>0 and  a) x=0b) x=2c) x=3 Important…

Q: Suppose that a point is moving along the path xy= 1 so that dy/dt=4. Find dx/dt when x=3.  dx/dt=?

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Q: find dy/dt. y = ecos2(πt-1)

A: We use the chain rule to find the derivative

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

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Q: Please solve the differential equation below. d²y(t) dt² +D dy (t) dt - + E y(t) = F dx (t) dt + G…

A: A differential equation is given by, d2ytdt2+D dytdt+E yt = F dxtdt+G xt with initial condition yt=0…

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: test whether the differential equations are exact and solve those that are. 2Y dy 0 dt+-

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Q: Suppose  y =    2x + 1,  where x and y are functions of t. (a) If dx/dt = 15, find dy/dt when x =…

A: Ans- (a)=30, (b)=1 .....detailed solution I have done ...hope you will get it easily...thanks

Q: Suppose that a = x(t) and y = y(t) are both functions of t. If y + xy – 3x = 23, and dy/dt = 1 when…

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Q: y? what is dt/dy? 2y +1 if t =

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Q: If r = sin ( ƒ(t)), ƒ(0) = p/3, and ƒ'(0) = 4, then what is dr/dt at t = 0?

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Q: given xy+x2y=2 such that dx/dt=2 in/sec. Find dy/dt for x=1

A: Consider the equation and

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

A:

Q: If L = 2x2 + y2, dx/dt = -1, and dy/dt = 3, find dL/dt when x = 5 and y = 1

A: Consider the provided equation and information,

Q: 2. Find dy/dx a) y = dt, x> 0

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

A: A

Q: + iwe¬lwt = 0. dt = 0,

A: Given differential equation is

Q: (b) If dy/dt = 2, find dx/dt when x = dx dt

A: By differentiating we solve the function

Q: a) dx dt dy dt =x+√3y+et √3x-y+e³t = ||

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Q: dy = 3 , find dt dx when x = 1 dt x and y are functions of a third variable t. If Væ + Vỹ = 4 and

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Q: Compute the derivative: d I/ In(t° + 1) dt dx

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Q: Use the method of first principles to show that d/dt(lnt)=1/t

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Q: If x'+y' +z-9, dx/dt = 5, and dy/dt = 4, find dz/dt when (x,y,z) (2,2,1)

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Q: Solve the IVP 3 d.x dx a(0) = 1, = 2. dt \t=0 dt2 dt

A: Given d2xdt2=-x(dxdt)3, x(0)=1, dxdt|t=0=2

Q: d²x dx + 4 + 5x – 10 = 0, when t dt 0, x = 0, x = 0 %3| %| dt2

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Q: If X+y = x-y x2. -y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0? О 12 O -12 12

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Q: Find the linearization of x = -1 f(x) = 3+ S sec(t – 1)dt at

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

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

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Q: 3 a) Find the exact integer value of a for which tsin (at)dt == ft sin (xt) dt = -². where a1. T

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Q: Suppose y = /2x + 1 , where x and y are functions of t. (a) If dx/dt = 3, find dy/dt when x = 4. (b)…

A: Differentiating with respect to t, we get

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

A: Topic:- application of integration

Q: x +y = x2 29) If - х - у + y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0?

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Q: dæ Let y = 3.75a + 4.75 and dt 0.2. dy dt Find when x = 3,

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Q: psin(z) (c) y = [ dt t+1

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Q: Find dx/dt when y=2 and dy/dt=3,given that x^3=9y^3-64

A: Find dx/dt when y=2 and dy/dt = 3, given that x^3 = 9y^3 – 64.

Q: If xy + z² = z, and dx/dt = -1, dz/dt = 3, find dy/dt when x = 2 and z = 4

A: Given: xy+z2=z and dxdt=-1, dzdt=3  Find dydt when x=2 and z=4 differentiate  xy+z2=z with respect…

Q: Consider a disease that propagates according to the system dx 3 357 — Зху — Зх dt - dy = X dt х*у —…

A: Given that, dxdt=357-3xy-3xdydt=x2y-13xy-68y The equilibrium points are,…

Q: dr Suppose dx dt dy 4, = 3. Find given that r = dt dt x = 8 y = 2 Write your answer in exact form,…

A: Topic = Derivative