2. If w In(4xy) = 2 - cos(2yz — 3), x = log(t), y = = : 4eª² and z = sin(ț³ – 1). Find dw dit

Q: If z = ln(2x+y), x = u sin v, y = v cos u, find az/av when u = 0, v = 1. A. -2 B. -1 C. 0 D. 1 E. 2

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Q: 8. (t² + 3) cos(5t) dt

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Q: What is the equation of the line tangent to the curve ev + cos(x) = 1 at the point (,0*? Y = 0 A B…

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Q: Find the following derivatives. Do not simplify your answers. d sin (3x) dx e²x + x² a)

A: NOTE: Refresh your page if you can't see any equations. . use the quotient rule for the derivative…

Q: d²y c. Find dx? if y= sin’0 , x= cos’e

A: We have y=sin3θ    and x=cos2θ We need to find d2ydx2 Now,  dydθ=3 sin2θ ddθsinθ=3 sin2θ cosθ dxdθ=2…

Q: 6. Find d(t) if a(t) = 2 cos(t), v(0) = 0 m/s, d(0) = 0 m

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Q: 4. A particle path is described by y = 4 cos (2x). dy a. What is an expression for as a function of…

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Q: Find i (t), given 7(t) = (5 cos(– 2t + 3), 4te', – 2t In( – t)). %3D F (t) =

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Q: 24.(cos t) y″ + (sin t) y′ − ty = 0

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Q: Ex. 14. Find Lt (cos Vr+1- cos Vx) x- 00

A: Introduction :

Q: 9. Find if x (t) = t + sin(t), and y(t) = t - cos(t). doe

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Q: Let a > 1 be a constant and y = (9e- sin z 3) In(x+a). Find y'(0).

A: Product rule of differentiation:…

Q: Let w = (sin(x) +7 cos(y)) dy ^ dz + (2³ – y cos(x)) dz A dæ + 14xyz da A dy. Find dw. dw = dx A dy…

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Q: 3. Let z = x?y + 3xy+ where x = sin 2f and y cos t. Use the chain rule to dz find when t = 0. dt

A: As indicated in the question, we will make use of chain rule of differentiation. Recall that the…

Q: dy Find dx if cos(x)cos(y) = sin(x)sin(y) + 3x + 3y – 2. O 1 O -2

A: Given:       cosxcosy=sinxsiny+3x+3y-2       cosxcosy-sinxsiny=3x+3y-2 We know that…

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Q: = dx 1. If 2y + siny = x¹ + 4x³ + (2π − 5), show that dy 16 when x = 1.

A: If draw the graph of Sin(y)= 2(π-y) , then we get only solution y= π

Q: (cos x-cosy-cotx) dx-sinxsiny dy=0

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Q: Q:3) Find for the following equations/ dx 3) y = log, cose"+ tan(In x) 4) x =t csc4t and y=t…

A: According to question given :(3) y=log3 cosex+tanln x(4) x=t csc4t and y=t cos(t3+2)

Q: If y = (2x² – 3x+4)(e¯* – cos 4.x), then find dy at x = 0 dx

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Q: 1. Find a differential operator that annihilates the function xe2 ( cos 3x + 3).

A: Given problem is :

Q: If Z= x Ln (xy) +y³ and y = cos(x²+1) find dZ ? dz dx

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Q: o(e) = La t -Va V1 + t²

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Q: Calculate. for z = 4x² + 3y², x = sin(t), y = cos(t)

A: We will use chain rule for total derivative  If z is a function of x,y . Where as  x and y are…