Given f(x, y) = sin(r + y) where x = st6, y = 5s – 6t. Find f.(x(s, t), y(s, t)) = f:(x(s, t), y(s, t)) =| Note: This question is looking for the answer to be only in terms of s and t

Q: Given f(x, y) sin(x + y) where x = s*t®, y = 3s – 6t. Find f.(æ(s, t), y(s, t)) = f:(#(8, t), y(s,…

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Q: Q. If z = f(x, y), where x = u cos 0 – v sin 0 and y = u sin 0 + v cos 0, with 0 a constant, show…

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Q: f z = e^(-t)(\sin x+\cos y), show that (∂^(2)z)/(∂x^(2))+(∂^(2)z)/(∂y^(2))=(∂z)

A: Given  z = e-t ( sinx + cosy)∂z∂x = e-t cosx,   ∂z∂y = e-t ( -siny ),  ∂z∂t =- e-t (sinx + cos y )

Q: Given f(z, y) = – 3z' + ry° + 5y², find fr(x, y) = | fy(z, y) = |

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Q: Q:Ifx = sin 6, y = 0,y= cos p6, prove that (1-x )y, xy,+ p°y= 0, dy and y1 d dy where y, %3! %3! de

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Q: If f(x,y,z)=sin(xy)+x2lny, then fxy at (0,pi/2) is equal to 1 FO

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Q: Given f(x, y) = sin(x + y) where x = s*t°, y = 3s – 2t. Find f.(x(s, t), y(s, t)) = f:(æ(s, t), y(s,…

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Q: By approximately how much will f(x, y, z) = x cos(rz) – 4x – 3y sin(xz) + y - change if the point…

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Q: If z = f(x, y), where x = r cos 0 and y = r sin 0, show that a²z 1 a°z 1 əz r дr дх? dy? дr?

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Q: If z= r +y, I= e' cos(s) and y= e' sin(s), then %3D 8z as at (t, s) = (1,0) is O-2e O 4e O 2e? 2e

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Q: Given f(x, y) = sin(x + y) where a s*t°, y = 2s – 6t. Find f.(x(s, t), y(s, t)) = fi(#(s, t), y(s,…

A: we have calculate the f_s( x(s,t) ,y(s,t)  and f_s( x(s,t) ,y(s,t)

Q: Given that F(x, y, 2)=sin xi+ cos yj + xzk. Evaluate F.dr where C is given by r(1)=(r.-r.1) : 0SısI.

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Q: dw Q/Answer the following - ar ,w = (x + 3y + z)², x = r3 – s², y = tan(r + s) ,Fsin(r+s) at the…

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Q: If f(z, y, z) = sin(z) +ay2-23 then the value of a that makes div(Vf) = -sin(z) - 6z is Answer

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Q: 2- find ow/ar if w = (x + y + z)², y = cos(r + s), at the point (r, s)=(1, -1) x = r - S, z = sin(r…

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Q: Y = w tan-1(uv), u = r + s, V = s + t, w = t + r when r = -1, s = 2, t = -1 1. as at ar as %3D

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Q: Given f(x,y) = ex cos y, Evaluate f,(0,2) (A) -sin 2 B) 0 C) e² D cos 2

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Q: Given, f (x, y, z) = sin (x²y – z)+ cos (x? – yz). Find fz. cos (x²y – 2) – sin (x² – yz) - cos (x²y…

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Q: Given f(r, y) = sin(r + y) where x = s't³, y = 4s - 3t. Find f.(z(s, t), y(s, t)) = fi(z(s, t), y(s,…

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Q: given sin -In\x+ y + 19| Ax, y) = V18 – (x + 11)² – (y + 10)² sketch domain p(-11+ v7, - 10) is…

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Q: Given f(x, y, 2) = In(x² + y? + z?), show that 2 dy? x² + y² + z²

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Q: . Evaluate ſſ,G(r)dA where G(r, y, 2) = arctan(y/x) and S is given by z = x² + y², with z< 9, r 2 0,…

A: According to the given information, it is required to evaluate the integral.

Q: Given f(x, y) = sin(x + y) where x = s°t2, y = 6s – 2t. Find f.(x(s, t), y(s, t)) = fe(x(s, t), y(s,…

A: From starting itself if we replaced x and y interms of s and t in f we can easily work in that.

Q: Let y, = sin(t) be a solution to t y" -y' +4 t y=0. If y(t) is the solution to the I.V.P ty" -y' +4…

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Q: Given f(x, y, z) = V 4a? + 2y? + z², find fz(x, y, z) = fy(x, y, z) = f:(x, y, z) = |

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Q: If z = sin(rry). and * = t+ s, y = t2² + 8 8z when t=0, s=1. at Find

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Q: If 1 Å : V(x2 + y?) [(хуz — Зху)а, + (zу? + 3x? )а, + ху а,] And B = r2 a, + sin 0 aø Find JÃ x B|…

A: The vector is A→=1x2+y2xyz-3xy ax+zy2+3x2 ay+xy az At P1, 2, 4, A→=152 ax+19 ay+2 az We know,…

Q: Given f(x, y, z) = V 42? + 6y² + 3z², find fz(x, y, z) = fy(z, y, z) = %D f:(x, y, z) =

A: we need to find out partial derivative of first order

Q: Given that f'(t) = 2sint + sec?t ,– t and f(0) = 4, find f(t) ドIN V V ドIN

A: Given, f'(t) = 2sint+sec2t  f(0) = 4 Formula used: Integral of sint = - cost Integral of sec2t =…

Q: Given f(x, y) = sin(x + y) where x = s°t, y = 3s – 2t. Find f.(x(s, t), y(s, t)) = ft(x(s, t), y(s,…

A: Given that: f(x,y)=sin(x+y)x=s3t2y=3s-2t

Q: find dw/ar if w = (x + y + z)?, y = cos(r + s), at the point (r, s)3(1,-1) x = r - s, z = sin(r + s)

A: Given w=(x+y+z)2 x=r-s y=cos(r+s) z=sin(r+s) point (r, s)=(1, -1)   when we differentiate partially…

Q: If z = x2 + y?, x = e' cos(s) and y = e' sin(s), then %3D dz at (t, s) = (1,0) is as %3D

A: Given that z=x2+y2, x=etcoss and y=etsins First we have to find ∂z∂s.

Q: Given f(x, y) = sin(x + y) where x = s°t4, y = 6s – 4t. Find f.(x(s, t), y(s, t)) = f:(#(s, t), y(s,…

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Q: Given f(x,y) = ex cos y, Evaluate fx(2,0) A cos 2 B) sin 2 C) 0 D) e²

A: fx is the partial derivative w.r.t. x

Q: For x, y E [0, 1], prove that 1 xy(1 – x – y) < 27

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Q: Find fr(r, y) and fy(x, y) given f(r, y) = tan r - cos(r² – y²).

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Q: Given that f(x) = sin a cos' r +2 (sin r + a)' +, the value of the constant and the least value of f…

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Q: Given f(x,y,z) = cos(3xy) + sin(3z). Find fy(5,5,0). Leave your answer correct to two decimal %3D…

A: Partial derivatives

Q: Given f(x, y) = 4e2" sin(2y) %3D then V f(0, 7) =

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Q: Given f(x.y) = e X cos y, Evaluate fx(2,0) e2 cos 2 O sin 2

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Q: Find fr(x, y) and f,(x, y) given f(r, y) = tan r - cos(r² – y³).

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Q: Given: f(x, y, z) = e¯ª sin(yz) Find: ² f(x, y, z) əyəx O z cos(yz) et O cos(yz) e O-ze-* cos(yz) O…

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Q: Given f(x, y) = sin(x + y) where x = = s*t*, y = 3s – 4t. Find - f.(x(s, t), y(s, t)) = fi(x(s, t),…

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Q: Find ∂w∂s and ∂w∂t when s = 1 and t = 2π for w = xy + yz + xz                    where x = s cos…

A: Given: w=xy+yz+xz where x=scos(t), y=ssin(t), z=t at s=1 and t=2π

Q: Find vf(x, y) if f(x,y) = e* c cos y 5.

A: Note : according to our guidelines we can answer only first question because there are multiple…

Q: So Evaluate F. dr where C F = (– 2z, – y, – 4x), and C is given by 7(t) = (sin(t), cos(t), t), 0 < t…

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Q: (a) z, and z4 where z = sin(2x) + y, x = s² – t², and y = s² + t² (b) z, and z4 where z = e*+y, x =…

A: We need to find the partial derivatives z.

Q: 2: find fr, fy, and fz. 9 f(x, y, z) = 1 + xy? - 222 5 f(x, y, z) = x - Vy² + z?

A: (a) Given f(x, y, z) = 1 + xy2 - 2z2 So fx = ddx(1 + xy2 - 2z2)    = ddx(1) + ddx(xy2) - ddx(2z2)…

Q: Given f(x, y) sin(x + y) where x = s*t, y = 4s – 2t. Find f.(x(s, t), y(s, t)) = fi(r(s, t), y(s,…

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Q: for w = x sin y +y sin x + xy. W yx Q2) A) Verify that wry

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