For f(x,y)=6x7 y6+2eX : (a) Determine fxx(x,y). 5 6 Answer: 252x°y° + 2y e (b) Determine fxy(x,y) . 6. 5 Answer: 252x°y + 2y²e*y + 2e (c) Determine fyy(x,y) . 7. 4 Answer: 180x'y + 2xe

Q: y? + 2xy + x³ = 3y.

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Q: dx 1) S- x(Vx+Vx?)

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Q: Tgir.y) = (2ry, 1+2+) and g(1.0)=8, then g(4.1)-9(2.1) =

A: Topic:- calculus

Q: 1. (D² -5D³)y = 4 2. (D³ – 5D* + 7D³ +D² -8D+4)y = 0

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Q: 16. (D² + 3D)y = -18x; y = 0, Dy = 0 when x = 0

A: Given differnetial equation ( D2 + 3D )y = -18x

Q: Find d²y/dx² for the following equatio: f) x2/3 + y2/3 = 1 g) x³ + y4 = 16

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Q: 3. Given 5y +4x² = 4x-y, find: dy dx a. b. d²y dx²

A: Derivative

Q: Find dy. 3 y=³√√x (6-5x).

A: Given query is to find differential.

Q: C=X+Xyz for y

A: Given,           w = x + xyz

Q: 5. (D²+4)y=4 cot 2x

A: We use variation of parameters method to solve the given differential equation.

Q: (0²+20+5)y= sinhx

A: D2+2D+5y = sinhxcan be written as:

Q: I. Evaluate the following: a. (x³ + cos y + 5 dy = - 3yx²) dx b. xdy – ydx = (4x2 + y2)dy c. dx +…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: xdy = (y - Vx² + y²) dx

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Q: 6. Find (x + 3y)dA where D = {(x, y) | æ² + y 0}

A:

Q: Solve: (x+y)dy-(x - y)dx=0 A. x² - 2xy-y²= B. x² + 2xy + y² =c C. x² + y² =c D. x² - 2xy + y² =

A: The given equation is(x+y)dy-(x-y)dx=0 To solve the differential equation.

Q: „ 2x2-5x if y= dx dy Find 5x3 +5

A: y = ( 2x2 - 5x ) / ( 5x3 + 5 ) y'=?

Q: dy as a function of x. Write the function in the form y = f(u) and u= g(x). Then find y = (- 2x +8)…

A: We know that ,  if y = f ( u ) and u = g ( x )  Then  dy / dx = f ' ( u ) • g ' ( x )

Q: answer the ff

A: 2. Given the differential equation,                        (1+y2)dx+(1+x2)dy=0.

Q: (X²y² + 1)dx +2x²dy =0 use the substitute xy=u

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Q: Change (x + 9)? + y? = 169 to x? + y? + Dx + Ey + F = 0. Change x? + y? – 8x – 8y + 16 = 0 to (x-h)?…

A: topic - equation of circles

Q: Solve (e²y - y) cosx = e sin2x dy dx Select one: O a ev + 2yev-e2cosx = c O b. e+ ye+e-2cosx = c Oce…

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Q: d. x+3y = 0 y-4+ 4(x - 2) f. -6x + 4y -7 Find intercent and v-intercent.

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Q: dy_ sec²y 1- 1+x² 2 when x=0 O y=

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Q: (y - x)(y + x)(y? + x2)(xdy- ydx) = x°dx

A:

Q: Find :a. b. 20 fő -1 20 dy (1+y) ² (20-6x) e 20x - 3x² dx

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Q: Find // (3x + 5y)dA where D D = {(x, y) | x² + y² 0} . Round your answer to four decimal places.

A: Double integration

Q: dz 4. Let r - y – 23 = 6ryz, then the value of is dr %3D 22 + 2ry (d) 코- 2yz 2 + 2yz y? – 21z (c) 22…

A: We are given: x3 -y3-z3=6xyz we need to find the derivative of z with respect to x. This can be done…