• Let f(u) = a'u = Li=1 a;Ui for a, u E R“. Calculate Vuf(u).

Q: Let y = tan(2x + 2). Find the differential dy when z = 5 and dr = 0.2 Find the differential dy when…

A:

Q: The linear approximation at x 0 to sin(2x) is A + Bx

A:

Q: find dy / dx by implicit differentiation.

A: In implicit differentiation, on differentiating y, we use dy/dx.

Q: The linear approximation at æ = 0 to sin(2z) is A + Bx where A is:| Previev and where B is: |…

A:

Q: Prove the formula for the derivative of a) (Inverse of cotangent) b) (Hyperbolic cosecant) y = csch…

A: formula for derivative of both function is following:-

Q: What is frz, fyy, and fyz of f(x, y) = In(y²")?

A: Given:           f(x,y)=lnyx2          fx=∂∂xlnyx2         Treating y as constant variable…

Q: Find dy for all of : dx 1- y = x/Inx у

A:

Q: If z = +3y, find the differential dz. dz =

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: dy Let ry = 1 and dt 5. dx when x = 5. dt Find

A:

Q: it Z = exY , where : x= Incutv) and y = tan () %3D find a) du శ్రీశర శశ్ర

A: Given,  z=exy ; where x=lnu+v and y=tanuv To find: partial derivatives

Q: : )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

Q: 7 show that: sech x dx = Sin (tankx). √1-u² multiply note: * & Sim'u = dx * you Cam سال dx sechx by…

A: Differentiate rhs

Q: What is the largest value that the directional derivative of ƒ(x, y, z) = xyz can have at the point…

A:

Q: Find fy ) for (x,y) Cos (x) sincy) exy

A: Given query is to find the partial derivative of the expression with respect to y.

Q: Show that if y = ex² dy cosh x then y(2x + tanh x) %3D dx Differentiate with resnert to y 1.

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

Q: Find dy/dx, where xsiny +ysinx=1.

A: Given - xsiny+ysinx=1 To find dydx Here we will use the following formulas- ddx(uv)=udvdx+vdudx…

Q: Find dy ду é^sinx in sx

A:

Q: 1. If y=tanx, prove that y=2(y² +1)(3y² +1).

A:

Q: F(x, y, z) = (6x° sin(y) + cos(18z), xº cos(y), – 18x sin(18z) + 6z°)

A:

Q: What value for a will make sinx { ,X # 0 2x f(x) = %3D 3D ,X = 0 a continuous function?

A: For a function f(x) to be continuous at x = a,limx→a-f(x) = limx→a+f(x) = f(a)

Q: gin (t) et dt

A:

Q: Find the total differential w = x2yz2 + sin yz

A: Partially differentiate w = x2yz2 + sin yz with respect to x and keep y and z as constants.…

Q: find dy / dx by implicit differentiation.

A: Given equation is x4y-8xy+3xy2=9. To find dydx. Solution: Power rule of differentiation states that:…

Q: If y = eex the y' - y" + exy' is equal to?

A: The given equation is y=eex

Q: Compute the differential dy  for  y=(6x+sinx)^3

A:

Q: x+y are functions of t.Ue %3D Ronphicit differentiation to express in terms af dx X and y dy

A: Explanation of the solution is given below....

Q: d - In(u²) dt dx et

A:

Q: 5. Use Implicit differentiation to find dy when y V x2 tya = 15x° +4siny 3

A: Using implicit differentiation find dydx for;  yx2+y2=15x3+4siny

Q: find fsubxz if (x, y, z) = ye^x + x ln z

A:

Q: TO Show Jv - x-V そーレ V+ dx

A: Jvx = ∑m=0∞ -1mx22m+vm! m+v!

Q: Compute the derivative of f (x, y) = (y + 2) + xysin(x) at (0,1).

A:

Q: y= sinh-lx then prove that Vx2+1 dx

A:

Q: By using caushy Rieman find the derivative of f(z) =Iz| if it exit ® fLz) = 2 +Z1

A: It is given that the function fz=z. The function fz=x2+y2. Note that, If the function is…

Q: Let sin(r-y) ||| + \y| +0 (x, y) = (0, 0) f(x, y) Is f continues at the origin? Why?

A: Solved below

Q: #2. Show that the line integral (sin y dx + (x cos y – sin y) dy)

A:

Q: If y= tanu, u=v-- -, and v=ln x, dy at x= e? dx what is the value of

A:

Q: 1. If y= tanx, prove that y"=2(y² +1)(3y² +1).

A:

Q: 1. Use implicit differentiation to find dy/dx when x 1 and y=1. у? + ху 3D 2.

A: Given y2+xy=2 when x = 1 and y =1

Q: +15 - If y = cos-1(x) , Prove that dy -1 %3D dx /1-x²

A:

Q: (a) If f(x.y) = e siny - e sinx then verify that fry fyz- %3D

A:

Q: Let y = tan(4æ + 5). Find the differential dy when a = 5 and da 0.2 %3D %3D

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: Show that the function f(z)=sin x cosh y+i cosx sinh y is continious as well as analytic every…

A:

Q: Sin'z dz 4.

A: Note :- These are multiple questions and you not mention here whose solution you want. So i am…

Q: er dy %3D sec da

A: The given differential equation is exdydx=sec y and the initial condition is y0=1. Solve the given…

Q: Find the integrating factor μ(x) of y' + 4y - tan(x) = 0 such that μ(0) = 1. μ(x) =

A: See the details solution in below

Q: 19. Sobve (1-x*)-+m*y=0 dy=m dx where x=0, y=0,

A:

Q: dy by implicit differentiation of 2r2 3y2 = 4?

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.