If x, y and z are independent variables and f(x, y, z) = x sin(y + 3z) of then find ôz .

Q: f z = e^(-t)(\sin x+\cos y), show that (∂^(2)z)/(∂x^(2))+(∂^(2)z)/(∂y^(2))=(∂z)

A: Given  z = e-t ( sinx + cosy)∂z∂x = e-t cosx,   ∂z∂y = e-t ( -siny ),  ∂z∂t =- e-t (sinx + cos y )

Q: Find dz/ax andðz/@yif I z = x* sin(xy³).

A: If a function f(x, y) is to be partially differentiated with respect to x, then we treat the…

Q: Solve for the general solution of (cos x cos y – cot x)dx – (sin x sin y)dy = 0.

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Q: x - y | 1 If c = 2, show that z = sin satisfies the equation xzx +yzy = 0. x+y

A: In the question it is asked to prove xzx+yzy=0.

Q: 4. If f (x, y) = sin(x)+e*y, find Vf (x, y).

A: Use gradient concept

Q: Given f(x,y,z) = cos(4xy) + sin(4z). Find f,(8,9,0). Leave your answer correct to two decimal…

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Q: x sin wx dx x2 + 6x + 10 Show that (2 sin 3w – 3 cos 3w) w > 0 %3D - 2e2w

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Q: Given that y1(x) = cos x is a solution to the ODE: (sin r)y" – 2(cos r)y' – (sin æ)y = 0 Then the…

A: The given differential equation is: (sin x) y''-(2 cos x) y'-(sin x) y=0Therefore:y''-(2 cot x)…

Q: Show that both y = sin x and y = cos x satisfy y" = -y.

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Q: (a) If y = tan x, prove that y = 2(y2 + 1)(3y2 + 1). (b) Find y' for y cos(sin?x). %3D %3D dy (c) If…

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Q: Find Y'and y" Y = sin (x²) Y = 2x² cos (x²) 2 y" = ? 2

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Q: If z = x sin y + y sin x a2z then дхду

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Q: Q1: If Z= x^3+y^4+(x sin y)+ (y cos x), Find Zxx? Zyy? *

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

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Q: z2 = - sin (z+y+2) ( '+ ) xy 3z + sin (x+y+z). dz -xz - sin (x+y+2) he he

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Q: If cos(4x – y) = x+y, then dx A -1 - sin(4x – y) 2+4 sin(4x-y) (B) sin(4x-y) 1 1+sin(4x-y) C) 1+4…

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Q: Given f(x,y,z) = cos(4xy) + sin(2z). Find f,(1,2,0). Leave your answer correct to two decimal…

A: We can find the answer as below.

Q: Find the general solution of sin x cos^2 ydx+cos^2xdy = 0  a. secx + tan y=C b. cos x cos^2 y + y…

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Q: Obtain the general solution to the equation dy dr 2+x COS x, y(0) = 2. 5.

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Q: b) Solve to find if y = Tant VE and t = 4x-2 – secx dz b) if z = sin20, and 0 = [cos(w) + 1]² + cos…

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Q: Suppose f(x, y) : where x = r cos 0 and y = r sin 0. 4 af af and ar Find when r 1, 0 -

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Q: Given, f (x, y, z) = sin (x²y – z)+ cos (x? – yz). Find fz. cos (x²y – 2) – sin (x² – yz) - cos (x²y…

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Q: 9. y = C,eax cos(bx) + C2eax sin(bx); a and b are parameters

A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other…

Q: Given that z and w are independent variable and dependent variablerespectively, obtain dz/dw b.…

A: Given that when cos(w − z) = z sin w

Q: If F(x,y,z)=sin(x³y²)+cos (Vxy2)+x®y²z, then fyz(1,-2,1)=

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Q: find ƒx , ƒy , and ƒz . ƒ(x, y, z) = sin-1 (xyz)

A: Given that f(x,y,z)=sin-1(xyz)

Q: Determine the General Solution of sin x sin y dx + cos x cos y dy = 0.

A: Given differential equation is sin x sin y dx+cos x cos y dy=0

Q: y = cos(2x), y = sin x, 0<x< 2

A: Solution is given below:

Q: Find the general solution of y''' − y'' − y'+ y = 1 + sin x + sin 2x + ex

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Q: Show that if y = V1 + sin x then sin x

A: We can solve it by doing derivative and make the proof.

Q: If ſ x sin x cos x dx = xsin²x + Ax + B sin 2x + C, what is the value of A + B?

A: The given integral is, ∫xsinxcosxdx=12∫x(2sinxcosx)dx=12∫xsin2xdx=12∫xsin2xdx=12I1

Q: What is if z = x²y+sin(ry²)? %3D dz = 2xy + y? sin(xy') az = x² + 2ay cos(xy) 8z = 2xy + y cos(xy?).…

A: The given function is z=x2y+sinxy2

Q: I. Eliminate the arbitrary constants -3x y= C, e sin2x + - 3x Cze cos 2x

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Q: Given f(x,y,z) = cos(4xy) + sin(2z). Find fy(1,2,0). Leave your answer correct to two decimal…

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Q: Determine c, and c2 so that y(x) = c, sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

A: Consider the function: yx=c1sin 2x+c2cos 2x+1. Calculate c1 and c2. Given yπ8=0 and y'π8=2.   Since…

Q: 1 (a) y = Va2 -- csc(2x) + 3 +1' (b) y = sin x

A: Compute the derivatives of the following functions (a) x2/3-cosec(2x)+1/π (b)( (x2+1)/sinx)3

Q: Find the general solution of y(4) + y" = 3t2 + 4 sin t – 2 cos t

A: Given differential equation is y(4) + y" = 3t2 + 4sin(t) - 2cos(t)

Q: What is if z = x'y+ sin(xy²)?

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Q: F(x, y) = 3x – 4y3 + 5x°ys + cos(x) – 3 sin?(y) |

A: Given query is to find the partial derivative onnf the expression.

Q: ди ди then x +y = u. 31. If u = Jy² - x2 sin-

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Q: ) // Show that y + y = 0, given that y = 2 sin x + 3 cos.x

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Q: if z=ex( x cos y-y sin y ), show that  ∂2z/∂x2+∂2z/∂y2=0.

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Q: Find constants A and B such that yp(x) = A sin x + B cos x is a solution of dy/dx + y = 2 sin x.

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Q: If f(x, y) = x²y + x sin y, then is af dx Select one: 2xy + sin y x² + x cos y ₂2 O O x² + sin y O…

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Q: Find the solution. dy sin x x +2y = y(2) = 1 dx , X A y = (4 + sin 2 + cosx²)/x² (B) cy= (3 cos 2x -…

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Q: f(x,y) = x² + 6xy − 3y² + 2x - 2y + 1433, g(x, y) = sin(x²y + 2x - 5),

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Q: Suppose f(x, y) = x2 + y? where x = r cos 0 and y = r sin 0. Find and whenr = 1, 6 -: = 1, 0 =

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Q: Determine cı and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

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Q: If Z= x^3+y^4+(x sin y)+ (y cos x), Find Zxx? Zyy?

A: Partial derivative of a function of two or more variables with respect to one variable is the…