Consider the function. Rx, y) = y + xe (a) Find Mx, y) dx. (b) Find M(x, y) dy.

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Q: Find df/dx and df/dy for the function.  f (x, y) = 2x2ey

A: given:  f (x, y) = 2x2ey

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A: let the function is f  first differentiate function f with respect of x df/dx then differentiate…

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Q: (y + Vx+ y)dx-xdy 0: when x= =DV3. y = 1 Note: use X - yv

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Q: f(r, y) : = V3x? + 4y? fz(3, – 2) =|

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

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Q: Let y = x2 – 4.x. With x = 5 and Ax = 1, find the values of Ay and dy. %3D %3D -

A: y=x2-4x , x=5 and ∆x=1

Q: Evaluate (2x - y) dx + (x + 8y) dy. C: x-axis from x = 0 to x = 3

A: To solve the line integral ∫(2x - y)dx + (x + 8y)dy over the curve C, which is the x-axis segment…

Q: a [2x – y 2.x dx [x +3y.

A: While finding partial derivative in multivariable function, if we have to find the partial…

Q: Calculate using polar coordinates: 1-x² x. y. √ x²+y² dy dx So So

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Q: 2. (3x +y)dx – (x+3y)dy = 0 2. y = 2 when x = 4

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Q: Evaluate the value of I = (4,0). I = Sleby. r 3x) dx + (6xe6y + y)dy, where I is the straight line…

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Q: Find fry for the function f(x, y) = x²? – xy? – 7y +3. %3D

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Q: Find the maximum value of the function f(x, y) = xye-(²x+3) in the first quadrant.

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Q: Find fyzy. f(x, y) = x°y® – 7x°y+x

A: Given: fx,y=x5y9-7x7y+x   We can write as: fyxy=∂∂y∂∂x∂f∂y So, ∂f∂y=∂ ∂ yx5y9-7x7y+x=∂ ∂ yx5y9-∂ ∂…

Q: Consider the function z = ƒ(x, y) = 9x3 - 8x2y + 4y3.;Find dz.

A: Consider the given function, z=fx,y=9x3-8x2y+4y3 The formula of the total derivative dz is,…

Q: d²y d²x - y = c1 g) dt? dt2 di h) L+Ri = E dt

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Q: Evaluate the value of I = f(e6 − 3x)dx + (6xeº + y)dy, r where I is the straight line from (0, 0) to…

A: On the curve Gamma , which is straight line from (0, 0) to (3,0) we have, y=0 and x  ranges from 0…

Q: d²y Given that x3 + y³ = 2, prove that 4х %3D dx2 y5

A: Given problem:-

Q: of af For the function f(x.y)= 7x-9y- 3, find and dy

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Q: Let z be a constant. Find the y" if y = v1 + 2zt + 5z't

A: Let z be a constant  To find y''if y=1+2zt+5z2t3

Q: find 5x² then find dy in terms of x and y. X If 3y - xy = 5x² then

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Q: Find the value of V. (V × A) where A = x²yî – 2xyz²j+ 2xy²zk.

A: The partial derivative of a multivariable function with respect to a variable is the derivative of a…

Q: Find Joy²dx + (xy-x²) dy along C: y = 7x from (0,0) to (1, 7).

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Q: Evaluate (2x – y) dx + (x + 6y) dy. C: x-axis from x = 0 to x = 3

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Q: dy : Find if dx 3.x 2) x - y 4+ y x +y 4) xy² x - y

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Q: Calculate dx y = x2

A: ddxxn=n xn-1