Let w = x³y cos(5z). Find the following. (a) g(x, y, z) = дw (b) Əy(x, y, z) = ду (c) o (x, y, z) (d) дw Әх дw (e) (f) ду дw дz = -(2, y, z) = (2,3, 2) = (2,3,0) = =

Q: Find the fay and fyy: f(x, y) = xe" - sin(xy) + x³y

A: fx,y=xey-sinxy+x3y

Q: Let w = x°y cos(4z). Find the following. a) (x, Y, z) = Əx b) (x, y, z) = dy c) dz (x, Y, z) · (d) -…

A: Topic = Derivative

Q: (a) fr = 4xz2, fy = yz and f; = xz 2 sin (x), fy = cos(x)y and f: = e" z z + y? If, f = = frâ + fyŷ…

A: a) Given f=fx+fy+fz and F→=fx x^+fy y^+fz z^ and  fx=4xz2, fy=yz, fz=xz So, we have f=fx+fy+fz…

Q: 3. If G = (2x²y – x*)î + (e*y + y sin x)j+ (x² cos y)k, find: %3D дхду

A:

Q: If flix.y)=XSin²(y)+y°Cos(x) prove that fn=2[Costy).Sin(y) ySin(x)]

A: First of all, we partially differentiate function f wrt. x and then we partially differentiate the…

Q: f(r,t) = cos(3r) exp(4t) %3D fi(x,t)+ frz(x,t) = f(r,t) %3D

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Q: Let cos(xyz) = 1 + x²y² + z². (a) Find y ?х' (b) Find az dy'

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Q: Let f(z, y) — (-(г + ))5. Then | 20(-(x+y))^3 dzðy dzðydz dz²dy

A:

Q: Question 9: Calculate r (t). r (t) = (4t, 2e2t + 1, 2 sin(t)) ®F(t) = (4t, 2e2ª – 1,2 sin(t)) O F(t)…

A:

Q: Evaluate . 2y2 cos(x) dx + 4ysin(x)dy where C is the line from (0,0) to G,0) and then a line from (,…

A: Line integral over the curve.

Q: Let g(8) = (2s – 1)°. Then g'(8) is 9'(1) is 9'"(8) is and g''(1) is

A:

Q: if y=sin (x), z=cos (x), v=exp(x), where could you plot y, z, v as shown below!

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Q: If v(r, y) is a harmonic conjugate of a harmonic function u(x, y) show that the function g(r, y) =…

A: Harmonic function: A two variable function ux, y is said to be harmonic, if the function is twice…

Q: For f(x1, x2) = x2 cos x1 find f'(x1, x2), f'(2,7) and df[(2,7); h]. For f(x, y, z) = (x – 2z)e"…

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Q: dz (2) Suppose z is a function of x and and suppose cos(32) xyz?. Find in Y, terms of x, y, and z.

A: The given function is, cos3z=xyz2

Q: Let f(z) = cos and g(z) = tan-(10z) Then if h(z) S(z) find: 9(z) h'(1) = N(즉) = |

A: The given functions are  f(x) = cos-1x/5 , g(x) = tan-110x   If, h(x) = f(x)/g(x)  Find h'(x) and…

Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t and x = sec-1t

A:

Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

A:

Q: Are fi (x) = x, f2(x) = x², and f3(x) = 4x – 8x2 linearly independent or linearly dependent on (-00,…

A: Definition: A set of vectors are said to be linearly independent, if no vector can be represented as…

Q: Question 8: The curve C in the ry-plane is parameterized by r (t). Find a parameterization of the…

A: Given:r→'t=4, 4e2t, 2costr→0=0,1,0

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

A:

Q: Q2- If Z = f(x, y) = sin(x³y5) Find fyy and fyx

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Q: If f(x, y)= cos(x +y), then- (+: O a. - sin (x + y) O b. - cos(x+ y) COS O c. cos(x+ y) O d. sin (x…

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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…

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Q: af Find and f(x, y) = 4xy – 6x? – y? + 9x – 3y + 3 - af af dy 3 f(x, y) = (4x – 6y)* fe af dy ||

A: Partially differentiate with respect to x and y. Detailed solution is given below.

Q: Find r'(t). r(t) = 4 cos (t)i + 2 sin° (t)j + k r'(t) =

A: