fx if f(x, y) = sin(xy) + x² In y cos(xy) – xysin(xy) 2 cos(xy) + xysin(xy) + cos(xy) – xysin(xy) + cos(xy) + xysin(xy) -

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

A:

Q: f(x, y, z) = xy°z +x*yz² – sin xy + cos yz Which of the following is the 1st order derivative of the…

A:

Q: Find f12(x, y) and f21(X, y) if f(x, y) = In (sin (xy)). O A. f12(x, y) = 1 - sin (xy) ; f21(x, y) =…

A: Given     f x,y=ln sin xyTo calculate:-  f12 x,y, f21 x,yConcept:- f12 x,y=∂∂y∂f∂x.…

Q: fyx if f(x, y) = sin(xy) + x² In y O cos(xy) – xysin(xy) – 4 cos(xy) + xysin(xy) + 2 cos(xy) –…

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: De min Jx when f(x, y) = cos(y – x) – x sin(y – x). 1. fr = -x sin(y – x) | 2. fa = x sin(y – x) 3.…

A:

Q: Example H·W: for f(x,y) = cos(xy) - x3 + y compute fxyy, fxxyy

A:

Q: Prove that = va² – x* if y =(f)sin~+ () + (9)v&* - x²

A: Differentiation wrt x

Q: Let z(x, y) be the function implicitly defined as the solution to 2x + y + z + sin(xyz) = 4 + that…

A:

Q: xyz 3. If f(x, y,z)= In| +e 2 find f,, f, and f..

A:

Q: If f(x) = A B C -S sec²x D tanx l+et sec 3x √1+1² 1+e' 1+e lanx -dt, then f'(x) equals tanx 1+e In…

A: The Leibniz integral rule gives a formula for differentiation of a definite integral whose limits…

Q: (b) Find the first order partial af and ду af Əx ay for the derivative f(x y) = 2x² sin(x+ )…

A: To find the df/dx of partial first order differential we differentiate function with respect to x…

Q: Find y': Oy: Oy = Oy' = O y' y cos(xy)+1 x cos(xy)-1 x cos(xy+1) y cos(xy)-1 y cos(xy)+1 x cos(xy)-1…

A: To find the value of y' for the given function.

Q: Let { sin(r-y) |r|+ |y| 0 (x, y) = (0,0) f(x, y) = Is f continues at the origin? Why?

A:

Q: If f(x) • cos ( z ) t'dt then f'(x) =

A: We can find the answer as below

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

A:

Q: f(x, y) = In (x²y - x) %3D

A: Here, the given function is: f(x,y)=ln(x2y-x) First to find the first derivatives:…

Q: fyx if f(x, y) = sin(xy) + x² In y

A:

Q: O Find all second order derivati ves for f(x,y) = Cos(2x) - x²e5Y + + 3y2

A:

Q: 2y y+cos x 2 + 2y + cosx Find f, if f(x, y) = (y)² COSX A O 2sinx (y)²secx + 2y + cosx C 1 (y)² + y…

A:

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: (B) If f(x, y) = x² ye(x+y²). Find the four seconed partial derivative.

A: Let us find the four second partial derivatives of the given function in the next steps.

Q: If U(x, y) = -e-Y sin x and f(x) = U(x, y) + iV(x, y) is analytic, then V(x, y) = Select one: O ey…

A: We have to find V(x, y) i.e.imaginary part of given analytic function,if we have real part is given.

Q: (xy(x²–y²) f(x, y) = { (x²+y²) (x, y) # (0,0) (x, y) = (0,0) ) show that fxy(0,0) f yx(0,0) Let

A:

Q: Find the partial derivative of z with respect to x z = (3x² + 1) cos(x²y). əz = -2x (3x² + 1)…

A: Given function z=(3x2+1)cos(x2y)

Q: let f( x, y) = x cos xy then fx is: is: O - sin y O -y sin xy cos (xy) - xy sin (xy)

A:

Q: Let z = f(x, y), x = rcos 0 and y = r sin 0. Evaluate the value of zg at the point (x, y) = (/3,1)…

A: Chain rule: If is function of and and are functions of and then, Given:

Q: а. f(x) %3D х3 In x + cos x b. f(x) %3D logs(3х3 + 2х + 1) ((5х+1)6 Vx2+x с. f(x) %3D In

A:

Q: Let f be a function with continuous first derivatives, defined by f (cos(xy), x2 + y³) xy If we take…

A:

Q: x-1, -1 sx< 0 0<x <1 x = 1 1<x< 2 2 <x<3 2r, f(x) = 1, -2r + 4, 0, Is f(x) is continuous at x = 1…

A: Given: f(x)=x2−1,−1≤x&lt;02x,0&lt;x&lt;11,x=1−2x+4,1&lt;x&lt;20,2&lt;x&lt;3 A function f(x) is…

Q: Let f(x, y) = y cos (xy), then f.(x, y) = fy(x, y).

A:

Q: c) Let f(x, y,z) = cos (xyz)sin(x²y=

A: The given function is f(x,y,z)=cos2(xyz)sin(x2y2z2) ..............(1) we have to find;  fx=∂f∂x=?and…

Q: 5. Let f(x, y) = sin(2.xy). Find f.(x,y) A) f,(x,y)= 2xcos(xy) B) f,(x,y) = 2y cos(xy) C) f.(x,y)= 2…

A:

Q: At what points (x, y) in the plane are the functions in Exercises 31–34 continuous?

A: Since you have asked multiple question, we will solve the first two question for you. If you want…

Q: a. F(x, y) = (x – y, x + y, z²)) b. F(z, y) = (2xy", 3x²y) O . F(r, y) = (1+ ysen(x), 1 – cos(x))

A:

Q: Example H-W:_for f(x,y) = cos(xy) – x³ + y* compute fxyy, fxxyy %3D

A: We have to find the partial derivative

Q: If f(x, y) = 3 sin(2x +y)- 4 cos(x - y) then the second derivative fee is a. -12 sin(2x +y) +4 cos(z…

A:

Q: Find fy for f(x, y) = (In x) (sin x² y). O fy = (In x)(cos x²y)(2xy) O fy = (cos x2y)(x²) O fy = (In…

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)…

A:

Q: Find the antiderivative F for f(x) = | sin z|, -T <x <0 satisfying F(0) = 1. (1) F(x) = - cos x – 1…

A:

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: 2. Show that fxy and fyx are equal for the function f(x, y) = x²y sin(x + y). %3D xy. cos(xry) + 2xy…

A:

Q: If ƒf (x) =¸ (A) (B) Sº sec²x 1+elanx In (secx) √✓ 1+tan²x tanx 1+e sec ³x tanx 1+e 1+1² tanx…

A: Using Leibnitz integral rule.

Q: What is dufferential equation of x'=4x-y and y'=-4x+4y when t=0, x(0)=1 and y(0)=1

A:

Q: Find an antiderivative F(x) of the function f(x)= 7sinx / 12+cosx such that F(0)=1.

A: Now,

Q: Find f-(x, y) and fy(x, y). f(1, y) = (y^tan(4x)) fa(x, y) : fo(x, y)

A: The given function is: f(x,y)=y5 tan(4x)-43

Q: Consider function f(x, y) = x cos(TxYy) + x³y. .3,

A:

Q: ди + 3x- = 1 + u, dx ди -co 0, dt u(x, 0) = f(x).

A:

Q: What is the partial derivative dv/dy of the following function? v = 3x + 9xy -y/In(z) + cos (z + x)…

A: