Assume x and y are functions of t. Evaluate for the following. dt dx y3 = 2x2 + 32; = 3, x= 4, y= 4 dt %3D dy (Round to two decimal places as needed.) dt II

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below. x 2−x−2=2y 2−2y

A: We have to find derivative of curve equation (implicitly).Curve equation is given by:

Q: Use Runge-Kutta 2nd order to find y at x=2, given that Fill in the table below with your result?…

A: Introduction: The formula of the second-order runge-Kutta method is given by, k2=hf(x0+h,y0+k1)

Q: Assume x, y, and z are functions of t with z =x+ y°. Find dz dx when = 4, and y = 5. dz |(Simplify…

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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: Find the differential of each function. (a) y = tan(7t) dy = 3 - v2 (b) у 3 3 + v2 dy =

A: topic - differential equations

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: Q4) Find dy /dx for the following functions: a) e*y = x – y b) y = (cos x)Vx

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Q: Find for each pair of functions. dy dt y=x² - 6x₁x=t² +1 dy * dt

A: Solving the problem by doing the derivative.

Q: Assume X and y are functions of t. Evaluate DY/DT for the following. y^3=2x^4+6; dx/dt=2, x=1,y=2…

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Q: dy For the function dt d y is 3 cos t, the third %3D order derivative dt3 O 3 cos t

A: Given: dydt=3cost To find the third order derivative d3ydt3. Solution: We have, dydt=3cost…

Q: Let x+y = 100,if dx dy = 2, find dt when y-6 and x-8 %3D

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Q: dy Assume x and y are functions of t. Evaluate for the following. dt dx y = 2x* + 81; = 2x + 81; =…

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Q: Find the value of df dt for the following function : F (x, y) = xy? X= cost, y= sin t.

A: Given:- F(x, y) =xy2  x=cost, y=sint To find:- dF/dt

Q: Find the forocings: of 3t rt +4 t+t dt. dx x'(x-1).

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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: dy Find for each pair of functions. dt y =x2 - 4x, x=t? +8 dt II

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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: Find the indicated derivative. dx 13 x = 14 when t= 1, dy = 20; y = 19x+ = ? - dt dr 3D1 3D1 Please…

A: We at first find dy/dx at t=1. Hence we find dy/dt at t=1.

Q: Assume x and y are functions of t. Evaluate for the following. dt dx 3 3, х%3D1, у%3D2 3 '= 2x + 6;…

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Q: Evaluate dy/dt for the following: y3=2x4+6; dx/dt=2, x=1, y=2

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Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below

A: Given,

Q: Find dw/ dt at the given value for the following functio 1) w=x² + y°, x = cos(1), y = sin(t), at †…

A: The given functions are w=x2+y2, x= cost  and  y=sint and t=π. Evaluate w in terms of t as follows.…

Q: Given t = x + ex, find dx/dt

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Q: Evaluate dW at t = dt for the function W = xy x = sin t, y = cos t, z = t². 4 49л2 972 9x2 4 49л

A: Given: W=xyz,x=sin⁡t,y=cos⁡t,z=t2 Substitute the value of x, y and z in w , we get W=sintcostt2…

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 dy/dx, where y is defined as a function of x implicitly by the equation below. x4-3xy2=2

A: We have to find dy/dx of curve equation .Curve equation is given by:

Q: Find the differential of each function. (a) y = tan 7t dy = %3D 5 - v2 (b) у%3D 5 + v? %3D

A: we have to find the derivative of the following

Q: Find the differential of each function. (a) y = tan(v3t) dy = 5 - v? 5 + v? (b) y dy =

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Q: Find the differential of each function. (a) y = etan(nt) dy = (b) y = V4 + In(z) dy =

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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: Find for the equation below. dy dt

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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: Find the differential of each function. (a) y = tan(v 5t) dy = 5- v2 (Б) у- 5 + v2 dy =

A: Use the basic concept of derivative and chain rule than simplify.

Q: Find the value of df dt for the following function : F (x, y) = xy2 X= cost, y= sin t.

A: The derivative of the function df/dt is solved below.

Q: dy dy For the function dt 7 cos t, the third order derivative dt3 is %3D

A: derivative with respect to t first oder derivatinve dydt is ddt(y). (which is given in the…

Q: Find the differential of each function. (a) y = tan V3t dy = (b) y = 1 + v2 dy =

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Q: Find dy/dt using the given values. y = x - 3x for x = 4, dx/dt = 4. dy dt

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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: Function y U dy du dy du dx dx y = sin(3x²) cos(3x²) _y = V5x² – 4

A: Given: The functions y=sin3x2cos3x2 y=5x2-43 To determine: The inner function u, outer function y,…

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

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Q: dy Find for each pair of functions. dt y = x ? - 6x, x=? +4 dy dt II

A: We can find the answer as below

Q: Evaluate the following derivatives: a) d V1 +* + 1° a dt dx 7, b) 10 d dt dz sin(z) 14 +1 c) :/ Vi+?…

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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: Given y is the square root of x. Find dx/dt when y=2 and dy/dt= 1.75

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Q: If x2 + y2 = 100 and dy/dt = 4, find dx/dt when y = 6. (Enter your answers as a comma-separated…

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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

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