Compute cos(x) cos(y) dx – sin(x) sin(y) dy, where c(t) = (9t, 4t2), o sts 1. (Round your answer to five decimal places.)

Q: Let y tan(4x + 4). Find the differential dy when x = 1 and da 0.4 Find the differential dy when a =…

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Q: Obtain the general solution using separation of variables. dz = a(cos 0 dz + z sin 0 d0)

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Q: dw Find the value of- dt at the point (1, In 2 ,0) on the curve x = cos t ,y= sin t, 0 <t< 2n where…

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Q: 18. y = x/I - x?

A: Differentiation:- The derivative of a function of real variable measures the sensitivity to change…

Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (- 0.01) xe…

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 2nx - 1 cos 2 dy = ||

A: topic - derivative and differential equation

Q: Find the differential of the given functions. a) f(x) = sin(cos(22)) CoS %3D 2x b) g(x) x3 – 7x

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Q: dx/dt + 4x = cos(2t), x(0) = -1 Find x(t)

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Q: dz Use an appropriate form of the chain rule to find dt 1 8 cos x – sin ry; y = 9t t %3D SSEVS Enter…

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Q: dy 1. dx x(2 In x+1) siny+y cos y

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the differential dy of the given function. (Use "dx" for dx.) y = In (√9-x²) dy =

A: Given: y=ln9-x2 To find the differential dy

Q: y= A cos at a solution to y" + 3y = 0 such that y' (1) = 2? %3D

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Q: Find the total differential. w = e²y cos(7x) + z³ dw = (No Response)

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Q: If z = cos x - e¹, x = 1² + 1 and y = 5 + ln t, then equals: dz dt

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Q: 211 sin nx dx [ [1-cos2nx]dx t, where n %3D

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Q: x2 dy Find - for y = x dx -for y =x cos t?dt. sť dt. 2

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = x+3/2x-3

A: Quotient rule of differentiation:

Q: Find dy/dt, x=4 sin t; y=12 cos t* O 24 cos t O -24 sin t O 12cos t O -12sin t

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Q: Find dy/dt. 13) y = cos (nt - 19)

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Q: (a) Find the differential dy. y = cos(x)

A: Differentiate the given function with respect to 'x' and find 'dy'.

Q: ZX = 24, XY = 10, and YZ 26. Find cos Y. %3D 5/12

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Q: Find the differential dy of the given function. y = arctan(x - 2) dy dx

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Q: Q5. Evaluate the triple integral cos(y²) dz dx dy.

A: The given triple integral is;  Cos(y2), z from 1 to 3, x from 0 to y, y from 0 to sqrt(pi/2).

Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. A cosx siny = c B sinx cosy…

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Q: Let y = tan(3r + 4). Find the differential dy when T = 4 and da 0.4 Find the differential dy when x…

A: Given: Differentiate the above expression of 'y' with respect to 'x'.

Q: Find F′(x).

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

Q: Let y = tan(4r + 8). Find the differential dy when a = 3 and dæ = 0.1 Find the differential dy when…

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Q: Solve the DE Ssinx siny dx + cosx cosy dy = 0 by separation of variables. sin y A cos X B sinx cosy…

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Q: dx 2а — У dt fip dt x + 2 cos(t)

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Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

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Q: dz Use an appropriate form of the chain rule to find dt 1 z = 8 cos a – sin xy; x = - y = 4t t'…

A: This question is based on Derivative of Function.

Q: 2. F(x) = fr Cos t dt %3D

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Q: 1. e+sin z- COs I 2e-u(t)dt

A: Part(1):-

Q: Find the differential of the function. z = e-5x cos(9xt) dz = dx + dt

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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: 7. Calculate dy/dx at the point indicated: f(0) = (7tan O, cos O), 0=/4

A: Here we will use the concept of parametric equation and Derivative of parametric ewyations

Q: Find the differential of the function. Z = e cos(2nt) dz = dx + dt

A: Given,

Q: dy Given y³ In x + x¹e³y = sin-¹(xy), compute da

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Q: 6) g(z)= . cos(t) dt

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Q: Determine the numerical value of dF of the function F(x, y) = e-3y cos(nx) given that X = 1, y =…

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Q: dz Use an appropriate form of the chain rule to find dt 1 8 cos x sin ry; y = 9t t' Enter the answer…

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Q: Compute cos(x) cos(y) dx – sin(x) sin(y) dy, where c(t) = (9t, t2), 0 sts 1. (Round your answer to…

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Q: Find the differential of the function. Z = e-9x cos(2rt) dz = dx + dt %3D

A: The total differential of the function  is given by . So, to find , first we need to find the…

Q: If x = 2 sin* t and y = 3 cos* t, then find dy at t = %3D dx 4 а. 1.5 b. -2.5 с. -1.5 d. 2.5

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Q: (dr Ifr=a cos ti +a sin tį+ at tan 0 k, find dt dr at t = 0. dr?

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Q: Find the differential of the function. Z = e-8x cos(5xt) dz z = dx + dt %3D

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Q: If x = 3 sin* t and y = 2 cos" t , then find dy at t = dx 4

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Q: Find the differential dy of the function y = 4 sin (2x). Provide your answer below: dy=dx

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Q: Find the differential dy of the given function. (Use "dx" for dx.) y = 4x + (sin(x))² dy

A: The solution is given below

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

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