lf f(z, y) = 5ery + 1 sín (inr + y) + 2r + 3y, find-a-,-,-and

Q: 8y'' - 12y' + 5y = 6 cos t

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Q: 3. Find fz and fy where f(x,y) = In(x + y²).

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Q: f f(x,y) = 3x² – 9y², then the total differential of f at z = 1 and y = -2 is :

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Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y = 2rsine

A: Here, the total derivative rule used is: z=f(x,y)=x2y2 & x=2rcos θ , y=2rsin θ

Q: z 3e*3S,y 3z2 + sin(z)s G dx

A:

Q: Find fæ, fy, and fz. 4,5 f(x, y, 2) = 4z In (a*y° cos(5z))

A: We can answer all the three question as below.

Q: of of and dy 6. For the function f(x.y) = sin ° (6x - 5y), find of df dy II

A: In partial derivative when take the derivative with respect to one variable consider other variables…

Q: Find the differential of the function f(x, y) = 7x² + 8xy + 5y² at the point ( – 3, 5) using Ax = -…

A: To find dz and ∆z

Q: Find the differential dy. y = 5x2 / x-9       dy =

A:

Q: Find d3f where f(x, y, z) = ln(x + y − z) + cos(x2y)

A: As per the question we are given a multivariate function as : f(x, y, z) = ln(x + y − z) + cos(x2y)…

Q: (a) z = x2 + y² + xy, x = sin t, y = e'. (b) z = x2 + y², x = cos t + sin t, y = cost – sin t. %3D

A:

Q: Let y : 2x + 3x +4. Find the differential dy when x = 5 and dæ 0.3 Find the differential dy when x =…

A: Given, y=2x2+3x+4 Differentiating with respect to 'x', we get dydx=ddx2x2+3x+4=2×2x+3×1+0=4x+3…

Q: Q5/ Determine the total differential If Z = f(x,y) = x²y², x=2rcose, y=2rsinė

A: this is a problem of differential. Based on the general formula and concepts we will answer the…

Q: Q2. If f(x, y) = xy² + y²cosy + xsiny then a) y² - siny c) 2y + cosy a²f is дудх b) y² + cosy d) 2y…

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Q: #2. | Ax)dzx, f(x)= (sin z, 0srs a/2 |cosr, n/2< rSA f(x)dxr. f(x): #3.

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Q: 1 olve for the differential of y when y = sinxx, x=-, and dx=-. 2 3 A 2 В 4 C 2 D 4

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Q: The differential of the function f(x,t)= e cos(2 tt) at the point (x,t)= (0,1) is given by -2dx +2…

A: Topic- Application of derivatives

Q: find ∇f at the given point. ƒ(x, y, z) = 2z3 - 3(x2 + y2)z + tan-1 xz, (1, 1, 1)

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Q: Determine fzz, fyy, and fz for f(x,y,z) = x²y³z – y sin(xz) + e».

A: When the partial differentiation is done with respect to a specific variable, then all other…

Q: find ∇f at the given point. ƒ(x, y, z) = (x2 + y2 + z2)^(-1/2) + ln (xyz), (-1, 2, -2)

A: Given function is  Firstly, we find all first order partial derivatives of f

Q: Q3) f(x,y)= y'sin(2x)+x²(cos(y')) find fyyxy уууххху Q4) w(x,y)=x siny +x²- (2x²+3y)² find dw

A: It is partial derivative

Q: Q2// B :- If u+v3e"cos y and u- v=e' sin y find the Jacobain of the function alu,v at dx.yl (x.y)…

A:

Q: w = In(x²+y² +z²) x = cost y = sint z = 4E

A: w=lnx2+y2+z2, where x=cost, y=sint, and z=4t. Find dwdt.

Q: If f = 5xy2 - X³Y then find df at (1,1) dy %3D

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Q: Find fa, fy, and fz. f (x, y, z) = 3z In (x°y³ cos(4z)) fr = %3D fy = fz =

A: Given that , fx,y,z=3zlnx6y3cos4z find fx , fy and fz.

Q: Find the solution of Uxy - x²y = 0, Uy (0, y) = y², u(x, 1) = cos(x)

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Q: B. Find y). 1. y = cosh?x 2. y = x tan-1 x - In vx2 + 1

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Q: uxx+uyy=0; u1(x,y)=cos x cosh y, u2(x,y)=ln(x2+y2)

A: Given:

Q: Find fæ, fy, and fz. 4.5 f (x, Y, z) = 4z In(x*y° cos(5z))

A: To find the partial derivatives with respect to x ,y ,z.

Q: Let v(x, y) = cos(4x) sinh(4y). Find f(2)with Im(f(z)) = v(x, y).

A:

Q: Find fa, fy, and fz. f(z, y, 2) = z In (a*y cos(52)) z In (a*y* cos(52)) fr = fy = f2 =

A: First order Partial differentials

Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

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Q: Find fa, fy, and fz. f(x, y, z) = 5z ln(x³y³ cos(z)) fx = fy fz f₂ = =

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Q: xy cos y dA, R: -1 <xs 1, 0s ys

A: Given: I=∬xycosydA And R: -1≤x≤1 , 0≤y≤π As we know that: The expression for the integration by…

Q: i. y = x-% % -4Vx ii. y = x+Inx+ sin(3x) iii. y = x° cOS X y = x° cos x

A: Use product rule of differentiation

Q: Find fr, fy, and fz. f (x, y, 2) = z In(x*y³ cos(52)) 4.3 fa = fy = fz =

A:

Q: A) F(x,y) = (cos(x+ y) – y sin(x + y), –x sin(x + y)) 1 2т — у B) F(x, y) = ( - x – y’ xy – y² C)…

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Q: Ql: f(x.y)-y cos xy over the rectangle 0sxs , 0 sys1

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Q: 7y f(x, y) = tan -686xy/(49y^2+x^2)^2 aº f dy? 7(49y^2-x^2)/(49y^2-x^2)^2 dxdy a² f =…

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Q: Find fa, fy, and fz. f (x, y, z) = z In (x'y cos(22)) 5.4 fy = fz =

A: topic - partial differentiation

Q: 1. Find fx,fy,andfz f(x,y,z)=sin(xy)cos(yz2)

A: It os partial derivative wrt x y z

Q: a) z=4x²-9x²y+2y³, com x=2 sen(t) e y=cos (t); b) w=xe, com x=4t², y=5e²¹ e z=2t². c) z=x y²+2x²,…

A: Introduction: When the independent variables of a function is again dependent on a single parameter,…

Q: 4. Find and sketch the domain. (4a) f(x, y) = ln (x² + y² – 4) (4c) f(x, y) = /9 – a² – y? V16 – x²…

A: As per our guideline we are allowed to do 1 question or maximum 3 subparts at a time. Please post…

Q: ind the linear approximation of the function at the given point. x_ v) = -4 sinx+ 7 cos y at (0, 7…

A: Hey, Since you have posted multiple questions we will answer only first question.

Q: •ý -2ý +y= ě sinx %3D Ans: y=ě +2xě - ě sinx • ý -uý ruy = 12 /* %3D e 2X 2 ZX .2 +C2 X e + 20

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: Find fa, fy, and fz. f(x, y, z) = 3z ln (x³y³ cos(2z)) fx= fy= f₂ = =

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Q: -f(x,y, z) = 2z3 – 3(x² + y²)z + tan-1 xz , (1,1,1)

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Q: F(x, y, z) = (xy — 2², 2x+cos(yz), 2y² - sinz)

A: