Given f(x, y) = æ® + 6xy³ – 2y², find fzz (x, y) = fzy (x, y)

Q: Find fy (x, y) for f(x,y) ry

A:

Q: Find the extrema of f(x,y) = xy + 14 subject to  x2 + y2 = 18.

A: To Determine: Find the extrema of f(x,y) = xy + 14 subject to                         x2 + y2 = 18.…

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

A:

Q: 2x :S dr f(x, y) dy. f (x, y) dy. •1-x² f (x, y) dy. -V1-r

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: Find fzyæ. f(r, y, 2) = a'y"2³ + xy® + y°z %3D f zyz

A: Given f(x,y,z)=x^4y^7z^5+xy^6+y^7z

Q: Let f(z) = 5z2 + 4z. Find u(x,y) if z = 8.17 + 3.6i. %3D Round off your final answer in five decimal…

A: Please find the attachment for the details solution

Q: Find fzyr. f(x, y, z) = x³y5₂6 + xy³ + yºz

A: Given: fx,y,z=x3y5z6+xy3+y6z We have to find fzyx For fzyx we first have to find the partial…

Q: Evaluate /// (x + y – 5z) dV Where - E = {(x, y, z) | - 6 < y < 0,0 < ¤ < y,0 < z < x + y²}

A: The given integral is: I=∫∫∫E(x+y-5z) dV where E=(x,y,z) | -6≤y≤0,  0≤x≤y,  0&lt;z&lt;x+y2

Q: Find an antiderivative F (æ) with F' (x) = f (x) = 5 + 24:³ + 15z4 and F (1) = 0.

A:

Q: Find fryz from the functions f(x, y, z) = 4x³y² – e²y* ++ 4y – x16 %3D - |

A: To find the third order partial derivative of the function fxyz f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16

Q: integrate ƒ over the given curve. ƒ(x, y) = x3&gt;y, C: y = x2/2, 0 &lt;=x&lt;= 2.

A:

Q: Given f(x, y) = 3æ'y- 8ry. Compute: www dy?

A: This question can be solved using the concept of partial derivatives.

Q: Solve for the antiderivative of the function f(x) = C. *++3x + C A. ++9x+C B. 즉++9x +C D. 2x ++3x +…

A:

Q: 6) If F = (3x²y – z)i+ xz3 + y*)j – 2x³z²k, find V(V - F) at the point (2,1,0).

A:

Q: If f(x, y) = xy + 3xy2 then df find at (1,2). dy

A: The function fx,y=xy+3xy2 then we have to find ∂f∂y at 1,2.

Q: Find fz(x,y) and fy(x, y) given f(r, y) = csc yArcsin(r²).

A:

Q: Find fzyz. f(r, y, z) = x*y³zª + xy" + y°z f zyz

A: Given-  fx,y,z=x4y3z4+xy7+y6z To Find- fzyx

Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y+ ++ 4y – x16

A:

Q: Find fzyx. 8.8 f(x, y, z) = x*y°z® +xy³ + y°z f zyz ||

A: GIVEN: f(x, y, z) = x4 y8 z8 + xy5 + y5 z

Q: Find the total differential. w = (3x + 4y)/(y + 3z)

A:

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: b) Given z = f(x -y, 2x - 2y, 3x – 3y). Show that dz dz 0. ду

A: The solution is given as

Q: Consider the function f(x) = 3z10 + 3z° – 3z² – 4. Enter the general antiderivative of f(z)

A: Given function is : f(x)=3x10+3x5-3x2-4 We have to find antiderivative(integral) of the given…

Q: Evaluate f, xyz dV, where Q = {(x, y, z): 0 < x < 2y, 0 <y< 1, 0 < z < x+y}.

A: According to question,Q = x,y,z : 0 &lt; x &lt; 2y, 0 &lt; y &lt; 1, 0 &lt; z  &lt; x+y

Q: Find fzya. f (r, y, 2) = x°y*z" 5.8 + xy* + y°z %3D f zyz

A: Given data÷

Q: 4. Suppose that z = x³y, x= t², and y = t³, find . dt = 12t11 dt 11t10 b) = 10t° dt d) = 9t® dt

A: This question is related to differentiation, We will solve it using given information.

Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

A:

Q: Find f, and f,. f(x, y) = 13x In xy

A:

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

A: Please see the answer below

Q: Consider the finction f(x,y) = x² + xy – 5x – y+ 1. Then:

A:

Q: |dx + N(x,y)dy = 0 x² + y,

A:

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

A:

Q: Find fryz from the functions f (x, y, z) = 4x³y² – e²y* + + 4y – x16

A:

Q: - x'yt, show that fxy = fyx. 7,4 Given f(x, y) = et*

A: Given f(x,y) = e(x^4y^9) - x7y4

Q: Find fr, fy, and fz. f(x, Y, z) = 4yz In(6ry) fz = fy = f: =

A: Given: f(x, y, z)=4yz ln(6xy)

Q: Find fzyz. f (x, y, z) = x°y°z° + xy° + y°z %3D 6-

A:

Q: C(x, y, z) = 90 + 6x + 4y + z where x is the cost of 1 pound of one raw material, y is the cost of 1…

A:

Q: find given f (x, y) = e² + 2xy² – 4y at (0,3) af dy'

A:

Q: Given f(x, y) = y ln(5x 6y), find f-(x, y) = fy(x, y) =

A: The function is given by fx,y = yln5x-6y To evaluate : The expression of fxx,y and fyx,y.

Q: а. max f (x, y) %3D 4x + 3ху + у S. t. х+4y— 29 3D 0 х+ 4у — 29 — 0

A:

Q: Find the 2nd solution using reduction of order. xy" +y' = 0; y1 = Inx For the toolbar, press ALT+F10…

A: Just I have used the method of reduction of order and solve in detail and find that  Second solution…

Q: Find fr and fy- f(x, y) = fetlo dt f.(r, y) = fy(x, y)

A:

Q: 3. For x= In /t y=t2, find y'-y"when x=0.

A: To find: The value of y'-y" when x=0 . Given: The value of function are x=ln(t) and y=t2. Formula…

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

A:

Q: Consider the function f(x) = 4x° + 7x® – 9z³ – 10. %3D Enter the general antiderivative of f(æ)

A:

Q: 4) f(x,y) =Vx +y Ans. f.= +y Vx + y?

A:

Q: Find f (1, 1) S(x, y) = In( %3D Vx² + y²

A:

Q: © f(X,y) = x4 + 'onY -10 © w = x*y - 10yZ z³ + 43X – 7tan (4Y)

A: It is partial derivative

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.