whe F(x, y) = 9yi+ 9x2. y2 conservative

Q: f(x,y) = =dt V11-6t?

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Q: - f(x, y) = Vx5 + y5. Find f-(0, 0).

A: Given that fx,y=x5+y55.It is required to find fx0,0.

Q: y (z² + yf) dz – a (z² – y²) dy = 0 %3D

A: Use substitution

Q: Integrate f(x, y) = 4c®* - 0.5y using h = 0.5 with y(0) = 2 from x =0 to 0.5.

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Q: Find fy and fy. f(x, y) = 13x In xy fx = 13 In y %D

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Q: Q/ find the dy when y = (x+z)= リ=(メ+2)mx, %3D 2x Qul Fird dy すく e y= ノ

A: Answer

Q: dy Let y = (x2 – vx)4". Find using any method. dx -

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Q: Q4: If f (x,y,z) = x?y³ – y²z³ then fy = %3D -

A: Given,           fx,y,z=x2y3-y2z3

Q: Q) Find y" + 3y 5y at x-5 where y = xsin(1/cscx))

A: NOTE- AS THE SECOND QUESTION PICTURE IS NOT CLEAR SO I AHVE DONE ONLY FIRST QUESTION. IF YOU WANT…

Q: [F-dš where F = xỉ – y°j+(x+ y+z)k

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Q: d'y 2y If x + y = xy, show that dx2

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Q: Q4. If y= f (t) and x=f (t) d²y dx2 dy 3 and %D 4t dx2 dy By using chain rule, find dt

A: Chain rule is given by dy/dx=( dy/dt )× (dt/dx)

Q: dy * + 2(t + 1)y² = 0, _y(0) = - ip 1/8

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Q: find fy CX,Y) it (x,Y)=x2-8xy- 2y?

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Q: et f(x, y) = 14x² + 13y² %3D nd D = fzz · fyy – fây-

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Q: Determine the relative extrema of f(x, y) = 2x2 + y2 + 8x − 6y + 20.

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Q: f(z, 9) = 82" + 5y² + 4z°y+ e7=y of Calculate

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Q: Evaluate..(x+.2.y.)dA..„.where.D.is.theregron. sunded. by.the.paradoolas.yz2x.and.y..l+x. 2 2

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Q: Consider the function f(x) = 2x³ + 71° – 8z2 – 8. Enter the antiderivative of f(x) + C

A: To find the antiderivative means integration of the given function

Q: 4 J4- y ktx dy S[S( x, y) dA = [] 3 R 0 2- 2 2

A: Consider the given expression, ∬Rfx,ydA=∫04∫2-y24-yx2-x33dxdy This suggests that the region spans…

Q: Q4: Given: d²y =[f(x-t)dt -show that = f (x)· dx? y %3D .2

A: Differentiation of integration

Q: 33. f(x, y) = xr – 3xy² + 6y²

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Q: 3. (D2 + 2D + 1)y = 0; when x = 0, y = 1, Dy = - 1.

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Q: Find the I.F of 2y(x^2-y+x)dx+(x^2-2y)dy=0

A: Please see the answer below

Q: b) Examine f(x, y)= 2x² – 4.x+ xy – 1 for relative extrema.

A: b) Examine fx,y=2x2-4x+xy2-1 for relative extrema fx,y=2x2-4x+xy2-1 fx=∂f∂x=4x-4+y2 fy=∂f∂y=2xy…

Q: Q3:A/ Find: dy dy y 2 Vy (1 + Vý)² yV4y? – 1 |

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Q: Find relative extrema for f(x,y)=x^3 - 6xy + 8y^(3) - 2.

A: Question- Find relative extrema for  f(x,y)=x^3 - 6xy + 8y^(3) - 2.

Q: Find f2, fy, and f.- f(x, Y, z) = (4x² + 6y² + 3z²)¯05 fz = fy = f. =

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Q: dy + 2xy = f(x), y(0) = 4, where xp Sx, 0sx<< 1 f(x) lo, x 2 1 0 < x< 1 y = x 2 1

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Q: f(x, y) = Calcule fzz 3ze + 9y + E O 3e" O 3ye" O 3ze"

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Q: of find 4x + 9y of and dy For the function f(x,y) = %3D of dx ||

A: We can answer this question as below

Q: dy Find dz given that y = -2 – 8z². z=-3

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Q: y = secx prove that d² y dx +y 2y

A: For y=sec x, we need to prove that d2ydx2+y=2y3. Here,            y''=secx''      =secxtanx'…

Q: f(x, y, z) = V9 - x² – y2 – z²

A: The given problem is to find the surface for the given function of three variables. Given function…

Q: f(x,y)=x2+y3, where x=t2+t3,y=t3+t9find df/dt at t=1.

A: Topic:- application of derivatives

Q: Find the function​ y(x) satisfying d3y/dx3=36, y′′(0)=14, y′(0)=5, and y(0)=8.

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Q: xy W=Ze y=8+tZ-St (Hiw) at

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Q: Find fy and fy: f(x,y) = - 3 e 4x-5y f,(x,y) = D

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Q: F(x,y) = -41² - 2xy-4y² +z+y.

A: Follow the procedure given below.

Q: Find fr and fy for f(x,y) = I+y fz = /(r+y)? and fy = /(r+y)2

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Q: or f(x, y) a + y? – xy +1 -

A: Consider the given function as fx,y=13x3+12y2-xy+1

Q: Q3: 1f f (x,y) = 6x*y5 + 4x*y4 Prove that: f (x,y) * fxxyy fxx * fyy = 1

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Q: dy given that y= Vx² (x – 4) dx la) Find %3D

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Q: 18. Differentiate y with respect to x using A-method. a) y = x³ + 2x? - x+ 5 b) y = ax*, where a is…

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Q: dy Find dt y = 3t(21 – 5) $ II 히

A: The product rule of differentiation states that ddx[f(x)g(x)]=g(x)ddxf(x)+f(x)ddxg(x) The chain rule…

Q: F(x) = F' (2) , where (t4 - 3t2 )dt %3D d. Vt dt x2 dx

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Q: Sove the IVP y" + 2y' + y : if 0 4

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Q: Find the total differential. 6x + y w = 4z - 8y

A: The given function is: w=6x+y4z-8yw=f(x, y, z)

Q: f(x, y) = /32² + 3y fz(4, 5) = VT23 %3D

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Q: 0If z-x"f), show that xZ+JZy=mZ.

A: