06/ Let w = z - sin(xy) where x = t y = In(t) z = et-1 Find dw/dt by :- a- Using Chain Rule principles b- Expressing (w) in term of (t) then differentiating directly dw Ans./ a- dt aw ay ay at b- Substitute x,y,z in w then make dw/dt aw ax ax at aw dz az at then continue -- -

Q: 3.2= e'-ry ; I=t3 and y = t° %3D

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Q: 1 If f(x,y) = tan-(x y) with x= cos(2 t),y= then sin(2 t) " df can be calculate as follwos: dt O1.…

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Q: (a) express dw/dt as a function of t, both by using the Chain Rule and by expressing w in terms of t…

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Q: Find dy/dt if y=ln(t^2+1)/(squareroot of (4-t)

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Q: Let z = cosh t. Find the differential dz when t = In 3 and dt = 0.2 O 4/3 O 4/15 O 8/15 O 1/3

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Q: Q2: find dw/dt at given value point for the following function 1 1) w = x² + y², x = cos(t), y =…

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Q: Find the differential dy: y = In(sec² ( 3ª²–20+5 312-2x+5 O (E) None of the choices dy = 2 (x – 1)…

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Q: Let z = f(x,y)= x^3+ xy+ y^4    (a)  Use differentials to estimate Δz as x changes from 1 to 1.05…

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Q: Q4/ 2x 1- If z = f(x,y) and z = x²y³ + + 1. Determine the total differential. -"/2 2- Evaluate: 2 S*…

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Q: dz Use the chain rule to find Ət z = tan (x – 8y), x = s cost, y = e² •Int Se dz 1+(x²– $y}² dt dz -…

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Q: (a) express dw/ dt as a function of t, both by using the Chain Rule and by expressing w in terms of…

A: Given, 1. w = x2 + y2 , x = cos t,  y = sin t;  t = π  2. w = x2 + y2 , x = cos t + sin t,  y = cost…

Q: 02:- a. b. Let u=x²-2xy + 2y³ with x = s² lnt and y = 2st³. Find ou/Os and du/ît. find the total…

A: In this question, we want to find the partial derivatives and total derivatives of the given…

Q: Consider the following differential equation. (sin(y) - y sin(x)) dx + (cos(x) + x cos(y) - y) dy =…

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Q: A homogeneous string is stretched and its ends are at x = 0 and x 1. Motion is started by displacing…

A: The boundary conditions are y(0,t) = y(l,t) = 0 and initial conditions are y(x,0) = μ0sinπxl and…

Q: a) i. Express in terms of the unit step function, the piecewise continuous causal functions 0 5…

A: Since you have posted a question with multiple sub-parts, we will solve only first three sub-parts…

Q: Let y = 4x. Find the change in y, Ay when x = 5 and Ax = 0.3 Find the differential dy when x = 5 and…

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Q: t, 01 1 a.) f(t) [m (sh w + (cos w - 1)] cos wt + [[ -[sin sin OLL - cos w + sh w]]sin wet dw - 1…

A: Given the function is ft=t0<t<10t<0, t>1

Q: 16 tan- dx 1 + x? dv 19. 20. (1 + v²)(1 + tan¬1 v) Oe® do 2e-0 sin 0 do 21. 22. e tal dx 2хe dx 23.…

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Q: 2. Using laplace transforms solve for x and y: dx dy + dt dt 2dx dy + + x +y = 3 dt dt subject to…

A: The solution is given as

Q: 6. If V(x, y) = xsin x cos y + y² then, F-VV and it is equal to A. -ily sinx cos y sinx cos y]…

A: We can solve using divergence formula

Q: 1. Find of/ar, af/ay and of/0z (y- sin(x))² f(x, y) = (r - 1) (y+ 2) + S(1, y) = in(V + y²) + (z² +…

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Q: Show that sin(y) 2e-" sin(x)) + ( .cos(y) + 2e¬#cos(x), 2)e/ = 0 %3D is not exact but becomes exact…

A: We have to solve given problem:

Q: 6. Let z = 5e** sin y . Compute the differential dz. A) dz = 20et* sin y dx + 20e** cos y dy B) dz =…

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Q: Let y = 5√√. Find the change in y, Ay when x = 2 and Ax = 0.1 Find the differential dy when x = 2…

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Q: of Let f (x, y) = tanh-¹(x-y) with x=e" and y= usinh (t). Then the value of dt (u,t) =(4, In 2) is…

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Q: 7. A particle is moving along the curve y=x-2 where x and y are functions of t. Find dx/dt if dy/dt…

A: To find :  dx/dt from the given conditions.

Q: Let w = x°e4y cos(9z). Find the value of dwldt at the point (3, ln 5, 0) on the curve x = 3 cos(t),…

A: Given: w=x6e4ycos(9z)x=3 cos(t)y=ln(t+5)z=6tDifferentiating we…

Q: 7. By differentiation (and having a suitable choice of integrating constants) show that L. f(s) ds+…

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Q: A) If w = 2 y et* – In z where x = In(t² + 1), | dw y = tan-1 3t and z= e3t. Find by Chain Rule dt

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Q: 11. In line integrals, if x(t) has a derivative equal to 0, with y'(t) and z' (t) not equal to 0, A.…

A: To Select: The correct the option(s): 11. In line integrals, If x(t) has a derivative equal to 0 and…

Q: 1. Use the differential df to approximate the change in the value of f(x,y) from the point (1,0) to…

A: We will be using definition.

Q: Consider the following differential equation. (sin(y) – y sin(x)) dx + (cos(x) + x cos(y) – y) dy =…

A: A first order partial differential of the form  Mdx+Ndy=0 is exact if My=Nx.

Q: Consider the first-order differential equation y'=f(x,y) and a point (a,b) in the plane. Which of…

A: Consider the first - order differential equation y ' = f ( x , y ) and a point ( a , b ) in the…

Q: Find the differential dy: y = sin(x√³). Ody = COS cos (T√²³) [2√T™- 2 O 0 O (E) None of these…

A: A detailed solution is given below.

Q: Q4) B Let w = z - sin(xy) where x = t y = In(t) 2 = et-1 Find dw/dt by :- a- Using Chain Rule…

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Q: Suppose z = x2 sin y, x = 3s2 + 2t2, y = 4st. A. Use the chain rule to find az and as az as…

A: We will solve the problem applying chain rule.

Q: 8) Let z = y-x². Use differentials to estimate dz when x = 1,y = 5, dx = 0.03, and dy 0.1. !! %3D

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Q: Find the differential dy of the given function. y = x cos 2x dy Submit Anguer X

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Q: Let y = 4ĩ. Find the change in y, Ay when x = 4 and Ax = 0.3 Find the differential dy when x = 4 and…

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Q: (z - 1)dt + (1 – t)dz %3D

A: (4) Given differential equation is z−1dt+1−tdz=0......1. We have to determine the whether the…

Q: 1 transforms the equation x dy + y = xy2sin(x) into The change of dependent variable y = dx dv A.…

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Q: Assume x and y are functions of t. Evaluate dy / dt for 4xey = 8 - ln 64 + 6ln x, with the…

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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: ci. use laplace transforms to solve the inittial value problem: У' — y' – 3y = F (t), where y(0) = 0…

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Q: 6. Find S(3y – y³) (1– y?)dy sin ycos y 7. Integrate: J sin² y dy 8. Find 3 S(5 - 3y-5)²dy

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Q: 6. If z2 = x2y2 (where x, y, and z are positive), and dz then what is when x = 2 and y = 3, given…

A: Given problem:- If z2 = x2 y2 (where x, y, and z are positive), and dz/dt then what is when x = 2…

Q: Let y=3sqrt(x)Find the change in y, Δy when x=5 and Δx=0.2 Find the differential dy when x=5 and…

A: Given function is Change in y is calculated as follows. when x=5 and Δx=0.2

Q: n/2 dx 2xy + dy dt dt such that Show that the functional , 1 dt x (0) = 0, x (R/2) = - 1, y (0) = 0,…

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Q: a) Without doing any calculations, state whether the vector field: er sin2(xy) F = -V 1 + x*y4 is…

A: (a) Since ∇×∇=0 So, curlF=0 Hence, F is conservative field.