fyx if f(x, y) = sin(xy) + x² In y cos(xy)- xysin(xy) - cos(xy) + xysin(xy) + cos(xy) – xysin(xy) + cos(xy) + xysin(xy) -

Q: Find dy/dx for: y cosy = xy Y O -y sin y+cos y-x Y cos y-x Y -y sin y-x 1 cos y-x O O O

A: Given :y cosy= xy Use product rule of differentiation which states that…

Q: true false f(x) = R x −100 cos(t)dt and g(x) = R x π cos(t)dt are both antiderivatives of cos(x).

A: f(x) = R x −100 cos(t)dt and g(x) = R x π cos(t)dt are both anti derivatives of cos(x).

Q: Let f(r, y, z) = ln(x² + z) + y²e#² – cos(2yz). Find fzyr- %3|

A: Consider,                                                                 f(x, y, z) = ln(x² + z) +…

Q: 5. (xy² +y – x)dx + x(xy + 1)dy = 0 6. (1– xy)-²dx + [y² + x²(1 – xy)-²]dy = 0; when x = 2, y = 1 7.…

A: Since you have asked multiple questions, we will solve the first question for you. If youwant any…

Q: Let z(x, y) be the function implicitly defined as the solution to 2x + y + z + sin(xyz) = 4 + that…

A:

Q: Given (x+ y}* – ( x - v}² = x* + y^, find dy/dx using implicit differentiation. A. - 2- E. None of…

A: Given x+y2-x-y2 =x4+y4. We have to find dydx  using implicit differentiation.

Q: dy If y sin(cos.xr), then dx O 6x sin x' cos x O sin x cos(cos x) 0-sin x cos(cos x) O 3x sin x %3D

A:

Q: ch of the following is the result of differentiating both sides of the ation x sin(y)=In(x)+y² with…

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Q: Let v(x, y) = cos(4x)sinh(4y). Find f(z)with Im(f(z)) = v(x, y). I

A: Given function is v(x,y)

Q: xy' – 2y = -x* cos(x) y(T) %3D

A:

Q: (e) f(x) = sin(e*) + eco«(a) (f) f(x) = cos(x) In(5x) (x) S(z2) = ()" %3D - 1

A:

Q: Find y': Oy: Oy = Oy' = O y' y cos(xy)+1 x cos(xy)-1 x cos(xy+1) y cos(xy)-1 y cos(xy)+1 x cos(xy)-1…

A: To find the value of y' for the given function.

Q: For the relation siny – y² =x²y– x+x , is dx 3x²y+1 А. cos y – 2y –x T – 1 3x² + 2y – cos y cos y –…

A:

Q: f (x) = L{f(x)} being cos3t dt |

A:

Q: dy Y=sin x dx x O x(y +cos x ) = sin x +c O x(y - sin x ) = sin x +c O x(y +cos x ) = cos x +c O x(y…

A: topic - differential equations

Q: Evaluate: y +y = - cos X COSX A. y = 0, sinx + Ca cosx + x sin x 8. C, COSX + Ca casx t x cas X C. y…

A:

Q: b) f(x) = In(1 – 3x) %3D c) f(x) = cos(t³) dt

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: If U(x, y) = -e-Y sin x and f(x) = U(x, y) + iV(x, y) is analytic, then V(x, y) = Select one: O ey…

A: We have to find V(x, y) i.e.imaginary part of given analytic function,if we have real part is given.

Q: Find F′(x).

A: Given- Fx=∫02xcost4 dt To find- F'x Concept Used- The Leibnitz's theorem as  ddx∫gxhxft…

Q: Let v(x, y) = cos(4x) sinh(4y). Find f(2)with Im(f(z)) = v(x, y).

A:

Q: a) z=-3x y² + sen(x²y) 2x c) z=-In (x y³) e) z = x²ln(2x³y) b) w=2xz-3e²xy d) z=2e²y sen(x) f) z=…

A:

Q: Let f(x, y, z) = ln(x² + z) + y²e#z – cos(2yz). Find fzya.

A:

Q: z=ye^(xy) - e^(xy) sin x +xy, find əzləx * O y^2 e^(xy)-e^(xy) cosx-y sinx e^(xy)+y y^2 e^(xy)-y…

A: Given z=yexy-exysinx+xy

Q: Suppose x and y are variable (y is a function of x) that satisfy the equation Sin(x +y) =xy, What is…

A: We have to find derivative

Q: 2. Let L:= D2 - x-D+4x2. Verify that Ly 0 where y(x) = sin(x). %3D %3D %3D

A:

Q: f(x,y,z)= xy²z +x² yz? – sin xy + cos yz Which of the following is the first-order derivative of the…

A:

Q: Let w = x°e4y cos(9z). Find the value of dwldt at the point (3, ln 5, 0) on the curve x = 3 cos(t),…

A: Given: w=x6e4ycos(9z)x=3 cos(t)y=ln(t+5)z=6tDifferentiating we…

Q: Find fa, fy, and fz. f(z, y, 2) = z In (a*y cos(52)) z In (a*y* cos(52)) fr = fy = f2 =

A: First order Partial differentials

Q: Find fa, fy, and fz. f(x, y, z) = 5z ln(x³y³ cos(z)) fx = fy fz f₂ = =

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Q: The conjugate harmonic function v(x, y) of u(x, y) = In (x2 + y2) is *() + 1. 2tan -1 2tan-1 + C ()…

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Q: 21. xy' = 3y +x* cos x, y(27) = 0 22. y' = 2xy + 3x² exp(x²), y(0) = 5 = 4x* %3D %3D %3D %3D 23. xy'…

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Q: Let z = x*y + 3xy* where x = sin 2t and y dz find = cos t. Use the chain rule to %3D when t = 0. dt

A: z=x2y+3xy4where x = sin 2t and y = cos t We need to find dzdt when t =0 Let's use the chain rule :…

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…

A:

Q: Example H-W:_for f(x,y) = cos(xy) – x³ + y* compute fxyy, fxxyy %3D

A: We have to find the partial derivative

Q: Find the differential of the function f (x, y, z) = sin x?y³z4. %3D O 2xy³z* cos a?y³ zªd« O 2xy®z*…

A: Given f(x,y,z)=sin(x2y3z4)=ddx(sin(x2y3z4))We know that sin(x)'=cos(x)=cos(y3z4x2)*ddx(x2y3z4)

Q: 1. Let z = f(x, y), find for: and dy - - (a) e"y + z ln y = 0 (b) yz – sin z = xy

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

A:

Q: 3. Find the derivatives of y with respect to x: a) y = xe* - e* %3D b)' y = e(+x+2) c) y = e*(sin x…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Consider the functions z = -2e" In y, x = In (u cos v), and y = u sin v. dz dz (a) Express and du as…

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Q: Find f(x)

A: We have to find out

Q: F(x) = [,**dt COS x 1 %3D 19

A: Answer is given below

Q: Differentiate: y = 2sinx/e O a. y' = (cos x- sin x)/e O b. y = (2e*cosx - 2e*sinx)/e2x O c. y…

A: Please see the solution below.

Q: If U(x, y) = -e-Y sin x andf(z) = U(x, y) + iV(x, y) is analytic, then V(x, y) = %3D %3D -ey cos x…

A:

Q: Verify that y = x[cos (Inx)] is a solution of x²y" – xy' + 2y = 0

A:

Q: Show that g(x) = cos 2 =x+3 ™K(x, t) g(t) dt 0 || sin x cos t, 0≤x≤t Y sin texr

A:

Q: implicitly dx

A: Solved below

Q: Find of /dy if f(x, y) = y sin(xy) 1 + xycos(xy)csc(xy) csc(xy) B) xy cos(xy) + sin(x) A) O

A:

Q: The function f(z)=e² is: „(x.y) =e*sin(y) O contiuous in CO u(x.y) =e*cos(y) O discontiuous in CO

A: Use the property of complex function to break in real and imaginary part. Here also use the concept…

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.