Find if f(x, y) = x2 +2xy cos x .

Q: Differentiate the function. y = (cos(6x))* y'(x) =

A: Function given is - y=cos6xx Taking logarithm both the sides we get- logy=(log6x)x =xlog6x…

Q: Find dy/dx. x + cos(x + y) = y2

A: The expression dydx is the sign of differentiation. Differentiation of the given equation with…

Q: Find if x2y - sinx - cos y dy dx O dy da 2xy x² COS sin y 10.

A: Given: x2y-sinx-cosy=10. Now,                x2y-sinx-cosy=10Differentiating both sides wrt…

Q: Solve the DE: (cos y- cos x)y' +cos y sin 2x=0

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Q: find dy/dx. y = cos x/x + x/cos x

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Q: y' – 3y + 2y = cos(e-")

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Q: Find the general solution of y′−y=sin x + cos 2x using variety of parameters

A: Given that: y'-y=sinx+cos2x To compare the given differential equation with standard form of…

Q: 1. Lif f(x,y,2)=2exp(-5xyz)cos(15z) Find ôxôz

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Q: (c) Show that the function z -- eX sin yt ey cos

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Q: find dy>dx.

A: y=cosxx+xcosx Differentiate the above function with respect to x.…

Q: Which of these is the differential of y = x· cos x ?

A: From the given data:

Q: Consider - 2x 2) (² f(x, y) = e fxx + fyy = 0 cos 2y - e -2y cos 2x. Verify that

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Q: Use the appropriate form of the chain rule to find the derivatives. 7x2 + 7y? + z²; x = psin ø cos…

A: This question is based on Partial derivatives.

Q: Differentiate y = e*cos x У'3

A: To find the derivative of the function which is exponential in nature

Q: Use the appropriate form of the chain rule to find the derivatives. 5x2 + 5y? + z2; x = p sin o cos…

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Q: 4x + Vx Y = (a) 7x2 – 3 et (b) y = 7x³ cos x 19

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Q: Find dx/dt: x = 2[cos (t/2)]^2

A: x=2cost22

Q: If Z= x³ +y* +(x sin y) + (y cos x), Find (Zxx+ Zyy=?)

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Q: Differentiate. y = e cos x + Cos( ex)

A: Given- y=ecosx+cosex To find- The value of the derivative of the above function. Formula used-…

Q: Find general solution of ODE : y'+y=sinx+x

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Q: Take the derivative of this integral.

A: Given

Q: What is the annihilator for y=x e*cos 2x ?

A: Our Aim is to compute the annihilator for y=x ex cos 2x -(i)

Q: 2. If y = e-* cos 2x, then f'(x) = %3D

A: Given : fx = e-xcos2x

Q: find dy. = cos (x2)

A: Given- y=cosx2 To find- The value of dydx. Formula used- ddxcosx=-sinx.

Q: Find dy dx' i) f(x) = Cos2x Sin²x %3D ii) f(x) = log,(x' +4)* e-* /2x - 5 -3x iii) f(x): (6-5x)'

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Q: find dy/dx. y = x2 cos x

A: Here given function as Use the product rule of derivative

Q: 3x d. Evaluate dx COS cos (3t – 1) dt

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Q: Find by implicit differentiation: dx a. cos y =x+ y

A: Since you have asked multiple questions in single request  so we  will be answering only first…

Q: ution of y" + 4y = cos 2x b

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Q: find dy/dx. y = x2 cos x - 2x sin x - 2 cos x

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Q: If f(x.y)=sin (2x+y) then the derivative f, Is 2 cos (2x+y) a. b. cos (2x+y) c. 2 sin (2x+y) d. 2…

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Q: Find y' where y = cos (ze19 =) – gec = Cos ( xe-

A: on doing differentiation with respect to x we get option C

Q: find dy/dx. ƒ(x) = x3 sin x cos x

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Q: Find by implicit differentiation. dx 1. x3 – xy + y? = 7 2. x³y + y?x = -3 3. xy = x?y + 1

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Q: if z=ex( x cos y-y sin y ), show that  ∂2z/∂x2+∂2z/∂y2=0.

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Q: y = cos x, y= sin 2x, x = 0 and x = 2

A: Solution

Q: y" – 3y' + 2y = cos(e-*)

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Q: Find dy/dx by implicit differentiation: x3– 3x²y + 2xy² = 12 b. cos (x- y) = x а.

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Q: Find at the point (1,0) for cos xy + ye* = 0. dx

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Q: a. cos x dy + y(sin x - 1) dx = 0; when x = 7, y = -2

A: According to our guideline we are supposed to to do only the first question if you want any…

Q: b f sin'x. cos²x.dx ef cos(Inx).dx C-

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Q: Obtain the der a) cos(xy)=2y, find y'

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Q: Differentiate f (x) = (cos 3x)V* %3D

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Q: Use the appropriate form of the chain rule to find the derivatives. W = 5x2 + 5y? + z²; x = p sin o…

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Q: Show that Sx cos*x dx = (x² + x sin 2x +cos 2x) + c

A: Given: ∫xcos2x dx=14x2+xsin2x+12cos2x+C.

Q: i. f(x) = Cos?(3Vx) (using chain rule)

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Q: X cos (3x) dx,

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Q: Find dy dx (i) f (x) = Cos2x Sin²x

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