im(z,v) →(0,0) F(x, y).

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: Əw at = xysin(z2), x= s-t, y=s2, z t². Use the Chain Rule to find .

A: We know that derivatives of d(xn)/dx = nxn-1. And d(sinx)/dx = cosx  Here i attached the solution of…

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: integrate ​f(x,y)=x2−y over the curve​ C: x2+y2=4 in the first quadrant from (0,2) to 2,2.

A: The solution are next step

Q: Find d3f where f(x, y, z) = ln(x + y − z) + cos(x2y)

A: As per the question we are given a multivariate function as : f(x, y, z) = ln(x + y − z) + cos(x2y)…

Q: d²y dy dt + 81y = 0, y(0) = 9, y' (0) = 3 + 18- %3D %3D dt?

A:

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

A:

Q: 2, 0 1

A:

Q: Use the Chain Rule to find dz/dt. z = cos(x + 7y), x = 5t5, y = 3/t dz dt II

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: w In(x2 + y2 +z?), x = ue" sin u, y = ue" cos u and z ue", using chain rule at the point (u, v) =…

A: Given w=lnx2+y2+z2x=uevsinuy=uevcosuz=uev

Q: Integrate f(æ, y) = e2=² + 2y² over the domain {(x, y) | æ² + y? < 3}

A:

Q: tu+v dt In(t) f(u, v) = u-1 fy Find using the chain rule u = x +y³, v= 3y- 3xs

A:

Q: Aşağıdaki alıştırmalarda, f., fy ve fiyi bulun. 23. f(x, y, z) = 1 + xy² – 2z2 25. f(x, y, z) = x -…

A:

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

A:

Q: -dx. V1–16z² Consider For the u-substitution u = 1 – 16x², which is the new integrand in terms of u?

A: Given:-∫014x1-16x2dxTo find: new integration in terms of u by using the u-sbstitution, u=1-16x2

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: Use chain rule to find dz/dt z=cos(x+2y), x=6t^3, y=7/t

A:

Q: Evnlunte: (а) (- xy) dydx (b) dr(x-) dy, where y, = Va? - x?

A:

Q: Find fa, fy, and fz. f (x, y, z) = 3z In (x°y³ cos(4z)) fr = %3D fy = fz =

A: Given that , fx,y,z=3zlnx6y3cos4z find fx , fy and fz.

Q: Integrate f(x, y) = (x + y + 1)- 2 over the triangle with vertices (0, 0), (4 , 0), and (0, 8).

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Line WY bisects Line UV at Y. If UY = 2x + 1 and YV = x +7, find UV.

A: Meaning of biscsts is dividing into 2 parts .

Q: d²y z + y = e-2tsin(t) , y(0) = 0 and y (0) = 0 dt2

A:

Q: SI, (x2 + y2 + z²) dxdydz , where T: 0<x < v4 – x², 0 < y < 2, /x² + y² < z< J4 – x² – y2

A:

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: Integrate counterclockwise z + 6 dz, C: |z – 1|= 4 Z – 2 z + 6 dz 2 ||

A:

Q: Find fz and fy- f(x, y) = Te“ dt f„(x, y) %3D S,(x, y) =| %3D

A:

Q: integrate ƒ over the given curve. ƒ(x, y) = x + y, C: x2 + y2 = 4 in the first quadrant from (2, 0)…

A: We have to find the integral The parametric equation of given curve is

Q: xyz dV, where E is the rectangular box E = {(x, y, z) : –1 < x < 2,0 < y < 1, –3 < z< 0}.

A: ANSWER:

Q: Let f(x, y) = xcosy- y'e*y. fxy at (1,0)is equal to: %3D -2/3 -2 1 0.

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: a)Let z = x?y – y² where x = t2 and y = 2t . Find dz/dt at t=1 using chain rule.

A: Given query is to find derivative is nge chain rule.

Q: Y" - Y = { 2, %3D Ost Y(0) = Y'(0) = 0, %3D %3D t21

A:

Q: If f(z,y) = 3z² - 8y, then the total differential of f at z =1 and y = -2 is: %3D O df = 6 dz + 32…

A:

Q: Find fr, fy, and fz. f (x, y, 2) = z In(x*y³ cos(52)) 4.3 fa = fy = fz =

A:

Q: Find div (e" grad u x 7) u=x-y ex at (2,1,0) where and =(x²+1)i + sec¯¹(x² −y)j + 3y²zk

A:

Q: Using the Chain Rule, find dz/dt for z In(x? + y²) and x = t, y = t²

A:

Q: siven f(x,y,z) = sin (3xy) + 3xyz3. Find fxzy(3,2,2).

A:

Q: Find the differential of f(x, y) = vx2 + y³ at the point (1,2). df

A:

Q: F(x, y, z) = xyzi+ (2ry+2) j+y°z°k conservative?

A:

Q: f(z) dz where a inside r= z-a

A:

Q: u2-1 Given y = dy and u = Vx2 + 2, find dx %3D u3+1

A:

Q: ds Find where Vt +s = 2s . %3D dt

A:

Q: Find fa, fy, and fz. f(x, y, z) = 3z ln (x³y³ cos(2z)) fx= fy= f₂ = =

A:

Q: X+Z+3Siny X +2y-2

A:

Q: Use the Chain Rule to find dz / dt or dw/ dt.(odd) z = xy3 - x2y, x = t2 + 1, y = t2 -1

A:

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

A:

Q: F(x, y, z) = (xy — 2², 2x+cos(yz), 2y² - sinz)

A:

Q: dz dt || z = cos(x + 3y), x = 8t³, y = 9/t

A: By the use of chain rule we need to find the required derivative.