(a) How many nth-order partial derivatives does a function of two variables have? 2" (b) If these partial derivatives are all continuous, how many of them can be distinct? 2" (c) Answer the question in part (a) for a function of three variables.

Q: Taking Clairaut's Theorem into account, how many different partial derivatives of order 5 does a…

A: Given query is to find the numer of possible partial derivative.

Q: (a) Find out the first and all second order partial derivatives of the values of the f(x, y) = x'y –…

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Q: 7) Find all the second partial derivatives of f(x,y) = x³y% + 2aªy.

A: Second derivative

Q: If z=(X+Y) e and X-u * find the tollawing partial derivatives using Chain ruleo Express answers as…

A: Given, z=x+yeyx=u2+v2y=u2-v2 To find : ∂z∂u , ∂z∂v

Q: 3.2 Find the partial derivatives of f(x,y) = 3x°y².

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Q: 5. Find the first partial derivatives of w= In(x+2y+3z) %3D

A: The given function is w=lnx+2y+3z

Q: 5) Starting from the expression Cp- Cy = T use the appropriate relations between partial derivatives…

A: The amount of heat required to raise the temperature by one degree in one mole of the substance is…

Q: 5. A cuboid with the dimensions of 30cm, 40cm and 50cm was heated and each of 1 the sides expanded…

A: Solve

Q: Consider the partial derivatives f-(x, y) = 5x*y" – 9x²y, f,(x, y) = 7æ®y® – 3z*. %3D Is there a…

A: As we have, fx=5x4y7-9x2yfy=7x5y6-3x3   We know that, according to partial derivative, we take the…

Q: D. Detefmine first and Second order Partial derivatives of the fu nction:

A: We have to find the first and second order derivatives of given function.

Q: 2. The second order partial derivatives Fxx(x,y) of the function ( F(x,y) =x'y- In (x'-y)) equal .

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Q: 75. Find the value of ôz/ðx at the point (1, 1, 1) if the equation xy + z³x – 2yz = 0 defines z as a…

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Q: Both first partial derivatives of the function f(x.y) are zero at the given points. Use the…

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Q: 58. Find the value of ox/az at the point (1,-1,-3) if the equation xz + y In x – x? + 4 = 0 defines…

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Q: Enumerate and explain the Four Second Partial Derivatives of the Partial Derivative of z with…

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Q: Evaluate the first partial derivatives of the function at the given point. f(x, y) =(x+y)/(x-y);…

A: Differentiating with respect to x, treating y as as constant, we get Now at (1, -2)

Q: 5-8 Determine the signs of the partial derivatives for the function f whose graph is shown. ZA

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Q: How are second-order partial derivatives used in findingextrema?

A: We have to tell how we can find extrema using second-order partial derivatives   The second…

Q: 6. Minimize the material needed to create an open box with dimensions xyz and a volume of 108 in?.…

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Q: I need help finding all of the first order partial derivatives for the function

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Q: 1 Find the partial derivative with respect to y of the function (2 x – 3) (3 y + 1)i el-5 z+5). -5…

A: To find the partial derivative of the given function with respect to y (2x-3)1/4(3y+1)1/4e(-5z+5)

Q: Compute the first-order partial derivatives. z = 4y* (Express numbers in exact form. Use symbolic…

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Q: What is the Mixed Derivative Theorem for mixed second-order partial derivatives? How can it help in…

A: Mixed Derivative theorem:" If the function f(x,y) and its partial derivatives fx,fy,fxy and fyx are…

Q: Find the second-order partial derivatives of the function. Show that the mixed partial derivatives…

A: Given: Finding the first partial derivative of the function is with respect to x by treating y as…

Q: 58. Find the value of ax/ at the point (1,-1,-3) if the equation x+ y lnx +4 = 0 defines x as a…

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Q: 2. Are the mixed partial derivatives of a function always equal? In other words, do the derivatives…

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Q: 4. Find the first partial derivatives of the function. z= xsin(ry)

A: We will use the formula  (uv)'=uv'+u'v Given z=x sin(xy) Then the partial derivative with respect to…

Q: Find the four second partial derivatives. z = y3 − 5x2y2 − 3

A: we have to find the four second partial derivatives.

Q: a) Describe the curve obtained when we make y = 2 and z = √2 . af b) Represent on this curve the…

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Q: Find all the second order partial derivatives of the given function. ​f(x,y)=xy2 + yex^2+5

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Q: Q.3 Determine all second order partial derívatives of (5) w = In(x² + y²)+ 2arctan| Mention any…

A: Given that  w=ln(x^2+y^2)+2arctan(y/x) To find the secondary order partial derivatives

Q: (a) Consider the R² – R function defined by g(x, y)=y' -x* +3y² +x. Determine how many saddle points…

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

Q: if z=square root of 36-x2-y2, compute the partial derivatives: The partial derivative of 2z/x2 =…

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Q: Find all the second partial derivatives. f(x, y) = x6y − 3x3y2

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Q: Find all of the first order partial derivatives

A: fx,y=x4+6y-10 Partially differentiate the function with respect to x. fx=∂∂xx4+6y-10=4x4-1=4x3

Q: Both first partial derivatives of the function f(x,y) are zero at the given points. Use the…

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Q: Determine all second order partial derivatives of…

A: Given: w(x, y) = ln(x^2+y^2) + 2arctan(y/x) To determine all the second order partial derivatives…

Q: # 4. Consider the function f (x, y) = x²y + y3 at the point (1,-2). (a) Calculate the partial…

A: Given that : f(x,y) = x2y + y3  at (1,-2)

Q: 9. Find all the second partial derivatives of Z; given: a) Z = xy³In(3xe' )

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

Q: Find the first partial derivative wx, wy, and wz of (x + yw )2 –  ez  – 2 = 0  Make the solution…

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Q: 1) Think of a multivariable function that might model something in your own work, hobbies, family,…

A: Consider the temperature in a room, T=Tx,y,z which depends on the position of the point in a room,…

Q: If a multivariate function has continuous partial derivatives, the order in which the derivatives…

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Q: If a multivariate function has continuous partial derivatives, the order in which the derivatives…

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Q: 9. Find all second order partial derivatives of the functions given below. (a) f(x,y) = In(x + y)…

A: We have to find all the second order partial derivatives of the functions fx, y=lnx+y and gx,…

Q: Differentiate implicitly to find the first partial derivatives of z. 2x2 + 11y2 + 3z2 = 36

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Q: how many second partial derivatives does f(a,b,c,d) contain?

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Q: 5,2 4. Find all first and the second partial derivatives. f(x,y)=2x°y +x y

A: First order partial derivatives :fx=∂f∂x  fy=∂f∂ySecond order partial derivatives:fxx=∂2f∂x2=∂∂x∂∂x…

Q: Find both first partial derivatives. h(x, y) = e-(x* + y4) h,(x, y) = h,(x, y) =

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Q: 1 the value of ax/az at the point (1, xz + y Inx - x2 + 4 = 0 nes x as a function of the two…

A: Here the given that,  xz+yln(x)-x2+4=0 where x as a function of two independent variables y and z