(e) 3x E R, Vy E R, xy > 0. (f) Vx E R, 3y E R, xy > 0. (g) 3x E R, Vy E R, xy > 0.

Q: If f(z)=u(x,y)+iv(x,y), how do I determine dz? I have that the answer is dz=dx+idy, but I don't…

A: It's nothing to do with f(z)=u(x,y)+iv(x,y). Here z be complex independent variable. Hence , z could…

Q: zy dy de t 5/2/2/0

A: To evaluate : ∫032/2∫0xxy dy dx+∫32/23∫09-x2xy dy dx The general formula of integration is…

Q: 2 dydx + f(x, y)dydx

A:

Q: CoS z 5,⁰ √1+4t2 dt, find F'(x) 11. If F(x) =

A: The objective is to find F'(x).

Q: Compute DF(, ) of F(1, y) = (e" cos(ry), r² + y) %3D

A: Given function is F(x,y)=eycos(xy), x2+y Let  f1(x, y)=eycos(xy)f2(x, y)=x2+y

Q: af dy %3D Y Given f(x, y) = 17x² sin y then 17x2 cos y O -34x cos Y O -17x² cos Y 34x cos Y II

A: The function is given by fx,y = 17x2siny To evaluate : The expression of ∂f∂y

Q: √²¹ fő fő¹¹ (x + y + z) dz dy dx 0

A:

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: Evaluate f S S," x dz dy dx

A:

Q: Where f(x, y) y calculate (–1, 1) towards the point dv (-1, 3)

A:

Q: Can you help me step by step?

A: Differentiate both sides w.r.t. t. Apply product rule on the right side. Product rule: (uv)'=u'v+uv'

Q: dy If y = (t + 2t + 8) (6t² + 6), find %3D dt dy dt

A: The given question can be solved as shown in step2.

Q: Find dy/dx. X=sec(t), y=tan(t); t= 3 dy dy 2 а. с. dx 33 dx 3 dy b. dx 3 dy d. 3 dx 33

A:

Q: Show that S f(x,y) dy dx = , f(x,y) dx'dy. %3D

A:

Q: Find fr and fy- S(x, y) = /"9e" dt f.(r, y) : %3D f,(x, y) =

A:

Q: If f = 5x2y2 - XY2 then find af at (3,1) %3D dx

A:

Q: Q4/ 1- Evaluate: f/2fy sinx dy dx ди 2- If u = x² + ey² ,x= sin 2t , y = cost² find at

A:

Q: 2, 0 1

A:

Q: Verify that [(y- 2x \dx +(2xy +x*dy = [S -川- dA where C is the bounda ôy R defined by y = 0, x = 1,…

A: See the details solution in below

Q: 2 4 Differentiate cxprersion (use D for dy X y' w. respect tox

A: on diffrentiating with respect to x we get

Q: 3 If y= Vx (x-1), find dy (Use rules, not a de finition XP

A: Given:         y=xx-1       dydx=ddxxx-1    Apply product rule:         ux·vx'=u'(x)·v(x)+u(x)·v'(x)…

Q: Compute dy/dx using chain rule where y = (u^2+2u)/(u+1) and u = x(x + 1)

A:

Q: f(x, y, z) dx dz dy f(x, y, z) dy dx dz f(x, y, z) dy dz dx

A: Given ∫064∫x8∫08-yfx,y,zdzdydx So, limits of x from 0 to 64 limit of y is from  x to 8  limit of z…

Q: I-x² f (x, y, 2) dz dy dx 1-x² Jo

A: we have to find the region of integration

Q: What is fx , where f (x, y, z) = (sin yz)ez3−z−1√y ?

A: Given, f (x, y, z) = (sin yz)ez3−z−1y

Q: Find fx , fy and fz. 1 -1 f(x, y, z) = tan %3D \xy²z4, ().

A: Here we will find Fx,Fy,Fz;

Q: dy If y = 2sin 3t then aY is: dt

A: we know that, derivative of a^x = lna * a^x  so from this we will solve the quesiton

Q: (d) S (1, y) = sin (2), (x, y) # (0,0) 0, (x, y) = (0,0) (e) , r + y # 0 7+y x² + y = 0 0, f (x, y)…

A: Limit of a function: A function f is said to tend to a limit l as a point x, y tends to the point…

Q: If f(x,y) = e* cos y then fyy (0,) is fyy (0) is

A:

Q: || (z, y) dy de = f(r,y) dx dy 0. Jo Jo O Tryc

A: Solution: The objective is to select the correct option

Q: Find the moment of inertia with respect to x-axis the aarea bounded by 2y^2-8y-16x=0 and the line…

A: The moment of inertia is the rotational analogue of mass. The expression for moment of inertia is…

Q: S dy S f(x, y)dx

A:

Q: dy - f *P, = 7 dt y(0) = 4.

A:

Q: Let f(x, y) = 3e" sin(5y) af af dy

A:

Q: dy = 3 , find dt dx when x = 1 dt x and y are functions of a third variable t. If Væ + Vỹ = 4 and

A:

Q: z = √xy, dz dt t², y = -t² then 2 2 2t²) =?

A: We have to choose the correct option from the given options according to the given information

Q: dy اذا كانت y = 3z2 + (sin(z وكان = *3ez؟ 4 : أحسب dx

A:

Q: If f(x, y) = 3x? – by, then the total differential of f at x = 1 and y = -2 is : O df = 24 dx – 6 dy…

A:

Q: dx Find the value ofat y=2 if x=z³+5z and z= dy (y² + 2y)'/³. -

A: Consider the function, x=z3+5z Differentiate 'x' with respect to 'z' as, dxdz=ddzz3+5z=ddzz3+5ddzz…

Q: (1, y' + 5y = f(t), y(0) =0, where f(t) = 0st<1 %3D t21

A: Solve the intial value problem using Laplace transferoms

Q: , find dy/dx. х • 7x² V2 + cos³t dt 126. y 125. y = V2 + cos³t dt 128. y 127. y = dt 12 + 1 dt 3 + A

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Find dy/dx y = sec u, u = X- COS X -

A: Given : y = -secuu = x-cosx

Q: e.) ay dy t (x³liny-x) dy = 0 %3D

A: To find: The solution using Bernoulli's method. Given: The differential equation is 2ydx+x3 ln y-x…

Q: dy zsin(x) dz

A:

Q: cos y f(x, у, z) -D xz2 XZ

A:

Q: What is the I.F of dy/dx=(y+y^2)/x?

A:

Q: ex+y+Z If f(x, y) = x+ey+e²> then the %3D ex+eY +eZ > value of fx + fy + fz is equal 2f f

A:

Q: If y= V (x-1), find dy (Use rules, not a de finition ) Xp

A:

Q: D SS f(x,y,z) dV = f(x,y,z) dx dy dz

A:

Q: Admit that for all (x, y), af (х, у) — х dx se (x, y) = 4y ду calculate g' (1) = f(2 cost, sint).

A: We have to prove 4y*f'x - x*f'y = 0 Also calculate g'(t).