If f(x, y) = e®¤ . In(16y), then fræ is given by: O 144 e9 In(16y) O - 81 e9 ln(16y) O 81 e9 In(16y) 144 e9z In(16y)

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: If z = xe" and x = t2, y = Vt then the value of dz at t = 1 is equal to . dt Select one: True False

A: Solve the following

Q: dy sec (re ), y(In 4) = 3 / t dt

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Q: dz/dy for z = e^xy

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Q: If f(x, y, z) = ln(xª + yl0 + 2³) + V (x10 + y8 + z4), then find fr, fy and f; at (1, 1, 1).

A: The given function is fx, y, z=lnx4+y10+z8+x10+y8+z4 and the given point is (1, 1, 1). Evaluate fx…

Q: Iffis of class c? and z= f(y.x), con u= x°y°,v = 5x+1. Verify that| :4xy kxy+ 4x³y° + 10xy- af дхду…

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Q: dy Find at t = a where dt 1 7. у %3D = 3s + 2 and s t2 when a =1. + 4

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Q: Compute /. x² dx dy dz, where E = {(x, y, z) : x² + y² < 1,0 < z < 1}.

A: To evaluate ∬∫Ex2dxdydz, Where E is the region E=x,y,z:x2+y2≤1, 0≤z≤1.

Q: dy for y= In(In(2r')) dt

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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: Assume w = x2y4, where x and y are functions of t. Find dw&gt;dt when x = 3, dx&gt;dt = 2, dy&gt;dt…

A: Given:  w = x2y4, x and y are functions of t  To Find: dw/dt when x = 3, dx/dt = 2, dy/dt = 4, y = 1

Q: Evaluate sczxay) dx^ (x+ 3y) dy along the poth C: ure on y =1-3 from l0,)) to Cl,0)

A: Line integral problem......

Q: dz is equal to .. dt Let z= In (x2+y²) where x=ue"sin t and y = ue"cos t. If u= -2 and t=0 then -

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Q: dw If w = f(x,y,z) = In(x² +y² z?),x = cost y= sin t ,z = 4VE , then is : dt + ww.

A: Given  w = f(x,y,z) = ln(x2 + y2 + z2) x = cos(t) , y = sin(t) and z = 4t Substituting the values of…

Q: If x =0.71 and y = 0.67, then value of C in the xsin-(x) V1-x² antiderivative of F(x) = is

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Q: 6. Ifw = f(x-y, y-x), then show that, ar + L = 0. dx ay

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Q: when (x, y, z) = (2, 2, 1). dt dz dy If x2 + y2 + z2 = 9, dx 8, and dt 4, find dt %3D %3D %3D dz dt

A: differentiate the given function with respect to 't' 2x dx/dt +2y dy/dt +2z dz/dt =0 Now substitute…

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: COS f(2, Y) af af dy f(x, y) = log, (3x) af %3D fe dy

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Q: If y = In(2x+3) , then find dy at x = 0. dx

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Q: 3. Given f(x,y) = xy + y2 +1° ey Verify that fry = fyx %3D

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Q: What is the integrating factor of the linear DE of order one ydx + (3x - 2y +5) dy=0,

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Q: 3) f(t)=t cosh(at) Ans. F(s)= s' + a? %3D 5) f(t)= 2te' Ans. F(s)= (s-1) %D 2.

A: We find Laplace transform of given function

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

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Q: If F(t) d [F(t*)] is equal to is an antiderivative of f(t), then dt

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Q: f [Mesin(2x) dx = e$in(2x) + C, then the M is equal to- If

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Q: Find the most general antiderivative of f(x) = 7e" – 8 sec? (x), where ř < x < 5.

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Q: 2. If f(x,y)= te Vy of=D0 then show) that 49 c) of af =0 dxay

A: Consider the given function. fx,y=1yex-y24y (i) First, we have to show that ∂2f∂x2-∂f∂y=0. First,…

Q: Eval S fCx,y,z)dV Por f auel regien W M, fory2)= 2x W: x'+ y? < zs 4

A: The region W : x2+y2≤z≤4, and f(x,y,z)=2x, we have to evaluate the value of ∬∫Wf(x,y,z)dV.

Q: The integrating factor of the non-exact DE: ydx – (x + 6y²)dy = 0 is

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Q: The radius r and height h of a right circular cylinder arerelated to the cylinder’s volume V by the…

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Q: a/ tangent s lope rasinczo) ) when e zT 9. 父 A dy do 2 517 dる 2. fhe D not of tne above

A: Given,  r=sin (2θ) Recall:  Slope, m=dydx

Q: s continuous on la,b), then d f(x)dx = f(x) dx A) True B) False

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Q: Evaluate dw/dt at t=9 for the function ​w(x,y)=ey−ln x​;  x=t2​, y=ln t. Options are: 1) 7 2)…

A: Given query is to find indicated derivative.

Q: Find the orthogonal trajectories of r^n= a^n cos . given that r(1) = 13

A: Hey there since you haven't mentioned any angle of cos therefore i am assuming it to be cos (n…

Q: Suppose that r = x(t) and y = y(t) are both functions of t. If %3D y = 2x/2 + 3, and dx/dt = 5 when…

A: The given function is: y=2x12+3

Q: 3y dx dy 1.) Evaluate exactly: Va + y?

A: We will use double integration

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

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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: If W = xyz with x = 2t*, y = 3t-, and z = 4t¬³, what is dw dt 24 O In(t)

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Q: *show work*

A: Find dy/dt.

Q: aw nd dt in term of t, if w = xy, x = cost and y = sint, when t = - %3D

A: Question 4 is not complete.  I am answering Question 5.

Q: Let f (x,y) = sin(xy) + x² ln(y). fyx at (0,) is equal to: %3D А. 33 В. О С. 3 D. 1

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Q: Let y 5x? + 4x + 3. If Ar 0.1 at I = 5, use linear approximation to estimate Ay

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Q: If f(x, y) = x cos y + ye", find the second-order derivatives %3D af a²f ах ду" and ar" dy ax'

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Q: dy 13. y(1) = e de ar(In y - Inr + 1)'

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Q: Assume x and y are both differentiable and functions of t. dy when x dt dx = 3? dt If y = x², what…

A: Explanation of the answer is as follows

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).

Q: what is (x fyx+ fy) given fCKiy)= ey

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Q: th 2 Evaluate khe fulawingcartesian integrat by changing theminte equiv alent Pelarintegrals: E 4-y…

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