Given the function: f(x,y) = x cos (xy) – x²e*Y - Find fa(x, y) а. b. fy(x, y) a fzy(T, y) C.

Q: Given f(x,y,z) = sin (2xy) + 4xyz³. Find fzzx(3,3,3). Answer:

A: Solving the problem by doing partial derivative.

Q: find af/ax and af/ay

A: f(x,y)=cos2(3x-y2) Now we take derivative When we take derivative with respect to x , we treat y as…

Q: Let X: EXP(0). suppose Y= 2x , the Y is i = 1 Select one: a. Gamma (n,-) b. Camma(n. 4) С.…

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Q: Given f(x,y,z) = sin (5xy) + 3xyz3. Find fzzx(5,2,3). %3D zZx Answer:

A:

Q: I. Evaluate the following: a. (x³ + cos y + 5 dy = - 3yx²) dx b. xdy – ydx = (4x2 + y2)dy c. dx +…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Find a function f such that Vf = 2e²x cos(5y)i - 5e²x sin(5y)j + z³k. f(x, y, z) =

A: Given :-  = 2e2x.cos(5y)i - 5e2xsin(5y) j + z5kNow,

Q: Evaluate . y? cos(x) dx + 2ysin(x)dy where C is the straight line between (0,0) and

A: The equations of the straight line joining (0,0)to π2,1 are x-0π/2-0=y-01-0=t(say) i.e. xπ/2=y1=t…

Q: Evaluate r(2) and r(-1) for r(t) = (sin 1,12, (1² + 1)~1). %3D

A:

Q: Let f(x,y) = In (x³y). If fx(6,2)=fy(5,a) what is the value of a? а. 1 O b.-1 O C. 0 O d. 2 O e. -2

A:

Q: Find a function f such that Vf = 2e²x cos(5y)i - 5e²* sin(5y)j + z5k. f(x, y, z) =

A: The given gradient function

Q: Given a function f(x, y, z) = cos (x + xy²z²), find: f#(5,1, 1) = frz (T, 1, 1) = %3D

A:

Q: Evaluate r(2) and r(-1) for r(t) =(sin~ t, t 2, (t2 + 1)- 1 ).

A: Given:rt=sint , t2, t2+1-1

Q: b.Introduce a new dependent variable v so that v = y/x, or y = xv(x). Express dy/dx in terms of x,…

A: Given that, v=yxy=vx

Q: Determine Du f{8,1.3) for f(x,y) = 4x?y + 2xy in direction of v = (-1,1).

A: Suppose f is two variables function of  x and y  .Then direction derivative of f at any point in…

Q: Find fyæy for the function f(x, y) = x² cos(y) +3\/y+ Vy + + Vy? + 3.

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

A: