Assume x and y are functions of t. Evaluate dt for 2xy - 2x + 4y3 = - 56, with the conditions = - 16, x= 4, y= - 2. dt dy %3D dt (Type an exact answer in simplified form.)

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: Find the differential of each function. (a) y = s/(9 + 4s) dy = (b) y = u cos u dy =

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Q: dy 2, find dt da when I = 1 dt x and y are functions of a third variable t. If V + /T 4 and |3D %3D

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Q: dA find dt dx 1 IfA%3D х? аnd 3 when x = 10, dt

A: our objective is to find the derivative at x=10.

Q: Compute the following derivative. [P(i+5j-5tk) (e'i + 5 e'j-3e -k)] dt [P(i+5j-5tk) (e'i+ 5…

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Q: Suppose y = (x + 1)5, and both a and y are functions of t. If. dy :1, find dt dx when x = = 1. |3D…

A: Given data:   The given function is y=(x+1)5. The first value given is dy/dt=1. The given value of x…

Q: Assume that all variables are the function of t. If 5x2 - 4y3+3y=D7 and dy/dt 2 when x-11 and y=3.…

A: Take the derivative of the given equation with respect to t and substitute all the values than solve…

Q: If x2 + y? = 169 and dy/dt = 5, find dx/dt when y = 12. (Enter your answers as a comma-separated…

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Q: dz dS 2 If S = z3 and -2 when z = 3, find dt dt

A: Derivative

Q: Assume that x =x(t) and y y(t). Let y = x +7 and %3D5 when x =4. dt xp dy Find when x = 4. dy dt…

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Q: . We are given r'y-5x+24y 6/ỹ, where x and y are both functions of t. If dx = 2, x= 1, and y=9, what…

A: Given query is to find indicated derivative.

Q: Assume that x and y are differentiable functions of t. For the following, find  dx/dt given that x =…

A: Differentiate both sides with respect to t. For xy use product rule, then cancel 2 from both sides.

Q: Assume x and y are functions of a third variable t. If xy = 20 and d = 10, find dy dt dt x = 4.…

A: u.v = uddx v + v

Q: Q: IF the value of (t) change from sin(“,) to cos( ",5. Find the dF for dx f(x, t) = V1+t³ Sa f(x,t)…

A: To find dFdx, whereF=∫αxβxfx,tdt, and fx,t=1+t3

Q: 2. Assume w=xy* , where x and y are functions of t. dw Find dt dx =2, when x=3, dt dy - 4, and y=1…

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Q: Given z=x²y+3xy, x=sin(2t), y=cos(t), find dz/dt when t=0

A: ddxcosx=-sinx

Q: Suppose y = v2x + 1, where x and y are functions of t. dx = 6, find dt dy when x = 4. dt (a) If dy…

A: Given y=2x+1 dydx=dydtdxdt

Q: In Exercises , find the indicated derivatives.9. ds/dt  if s = t/2t + 1          10. dy/dt  if y = t…

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

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: assume that x and y are both functions of t and find the required values of dy/dt and dx/dt.…

A: Given y = sqrt x =x(1) Given x = 9 and dxdt= 2∴dydt= 12x .dxdt by chain rule⇒dydt= 129 .(2) = 19…

Q: Find the differential of each function. (a) y = tan(V5 dy = 1 - v2 (b) у 3 1 + y2 dy =

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Q: Assume x and y are functions of t. Evaluate dy,dt for each of the following.:…

A: We have the given function in x and y as 2xy-5x+3y3=-51 On differentiating both of the side with…

Q: Find the differential of each function. (a) y = s/(3 + 2s) dy = (b) y = u cos u dy =

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

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Q: 4x - 6xy? + 3y² = 228; dx = 3, x = -3, y = 4 %3D

A: Given  4x3-6xy2+3y2=228 ; dxdt= 3   at     x=-3    , y=4

Q: The current in an electric circuit is given by the equation di Ri +L==0, dt - %3D where L and R are…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Assume x and y are functions of t. Evaluate dt y³ = 2x² +6: dx dt -=4, x= 1, y = 2 for the…

A: Please follow the next step.

Q: Find - given that dt dx x? + y? = 2x + 4y, x = 3 y = 1, and dt 11 dy i dt II

A: Given problem is :

Q: Assume x and y are functions of t. Evaluate dt dx 3 y = 2x +93, dt = 2, x = 5, y = 7 (Round to two…

A: Given: y3=2x3+93 ; dxdt=2, x=5, y=7.

Q: dT equation dt k(T A).

A: we have been given the differential equation dTdt=k(T-A) this is the first-order linear differential…

Q: Find dw/dt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

A: Find dw/dt (a) by using the appropriate Chain Rule and (b) by converting w to a function of t before…

Q: Assume that x = x(t) and y = y(t). Find dt using the following information. dy x² +y? = 2.92; - 2…

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Q: Evaluate: L{t f -t e2t Cos t dt}.

A: Evaluate: Lt∫0te2t costtdt First of all we find    L(cost)=ss2+1L(e2tcost) =…

Q: Determine whether the given equation is separable, linear, neither or both.  (t^2+1)dy/dt=yt-y

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Q: Evaluate dt dW at t=0 for the function W = e' – In x , x = t², y= In t

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Q: Solve the initial-value problem for a as a function of t . dx (t2 – 11t + 24) = 1, (t > 8, x(9) = 0)…

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Q: b.Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x,…

A: Given that, v=yxy=vx

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

A: SOLUTION-

Q: Assume that w= f(s° +t*) and f'(x) = e*. Find and dt D I3D 次咖一。

A: Finding the expression of w and proceed the differentiation

Q: Consider the function g(x) = 5 S cos t dt – x?. Then g' (x) is

A: Given gx=12∫x4x2costdt  -x2

Q: Find fr and fy- f (x, y) = 8e dt

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Q: Find fa and fy. f(x, y) = 4e dt %3D

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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: Find the differential of the function. V T = 4 + uvw dT du + |dv + dw

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Q: assume x and y are functions of t.  Evaluate dy/dt for the following: y3=2x4+6; dx/dt=2, x=1, y=2

A: The given function is  y3 = 2x4 + 6    ...... (1) dx/dt = 2, x = 1,   y = 2

Q: Assume that all variables are the functions of t. If 3y2-2x2+4y=2x and dy/dt =4 when x-9 and y=12.…

A: Given,  3y2-2x2+4y = 2x   and dydt= 4  when x = 9  and y = 12  Then, we have to find the value dxdt…

Q: Assume x and y are both differentiable and functions of t. dy when x dt dx = 3? dt If y = x², what…

A: Explanation of the answer is as follows

Q: Assume x and y are functions of t. Evaluate DY/DT for 4xy-4x + 6y^3 = -258, with the conditions…

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Q: Find the differential of each function. (a) y = tan(v7t) dy = 5 - v2 5 + v2 (b) y= dy

A: a) Given function is By using chain rule of differentiation , we have

Q: Find the differential of each function. (a) y = tan(V5t) dy = 5 - v2 5 + v2 (b) y = dy =

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.