If z-f (x y): then its total differential can be expressed as * (),中 (). dyds dy + dz O Option 2 O Option 1 ) O --). - ). dz - dy Option 3 O Oprion 4.

Q: Find both first partial derivatives. z = 15XVY 15xVy %3D dz az

A: We need to find partial derivative.

Q: dx/dt = 2 and y=x^3, what is dy/dt when x=-4,2,6

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Q: Evaluate. The differential is exact. (1, 1, 1) (-10x - 8x7y7) dx - 7xS6 dy + 54z5 dz (0, 0, 0) 3 4

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Q: find dx/dt at x = 3 if y = -5x^2-4 and dy/dt = -3. dx/dt =

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Q: Find both first partial derivatives. z= 4y?V dz az ду

A: We can solve the problem by partial derivative method.

Q: Verify the homogeneity of the differential dy _ y²-2xy x2 - 2xy dx

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Q: ,2x Calculate the second derivatives of function f(x) = sin(x) + Ide²x at point x = 0.625 using…

A: Three point central differential formula for 2nd derivative   f′′(x)= f(x-h)-2f(x)+f(x+h)h2 Five…

Q: Suppose z = f(x,y) is a differentiable function of two variables. What do the partial derivatives,…

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Q: Find both first partial derivatives. z = exy az ax dz II

A: topic - 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: Find both first partial derivatives, as well as fy for

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Q: find dx/dt at x=1 if y=3x^2+3 and dy/dt=1

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Q: Find dy/dt when x = 1 if y = x2 + 7x - 5 and dx/dt = 1/3.

A: Given:

Q: integrate dy/(sb - smy-bny-nmy^2

A: SOLUTION-

Q: Find the first partial derivatives with respect to x, y, and z. fx, у, 2) %3 4x?у - 2хуz + бу2?…

A: Given  f(x, y, z) = 4x2y - 2xyz + 6yz2

Q: dy Find at x = dt – 4 if y = dx - 2x2 + 3 and dt 2. - - dy dt ||

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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 the second order partial derivatives of xº + y° – 3 axy and 3 3 verify dxdy dydx

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

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Q: 2.Evaluate the total derivative of u with respect to x for u = 6x²+4y² + 4z² when y = cosx and z =…

A: We have to find total derivative of u with respect to 'x'    where     u = 6 x2 + 4 y2 + 4 z2  Given…

Q: Example: If Z=f(xiy) hoas continuous second-order partial derivative and x=r²+s? and y=rs, find

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Q: Find both first partial derivatives. z = cos(10xy) az ax az ||

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Q: Find both first partial derivatives. z 13XVY az az ду

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Q: +[2yln [2yin (3 3y²dx 3siny dy = 0 ;when x = 1, y = 0 5x x2+3x x+3,

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Q: y = x* Inx dy : =x³ +4x° Inx dx O Op tion 1 None of these dy - -x -4x° In x dx =x² -4x° Inx dx O…

A: Explanation of the answer is as follows

Q: Find both first partial derivatives. Z = 13xVy az %3D az %3D ay

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Q: 4. Get the exact a. dy = cos 2x dz differentials of y = (sin 2)² b. dy=sin 2z dz dy = sin 2x d.…

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Q: Compute the differential dz of the function. 3,,10 x°Y %3| dz

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Q: Find both first partial derivatives. z = 9xVy az az ду || ||

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Q: Find the solutton of followins ordinery differential e quation. yl- 2y' +y

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Q: 5) If y = x³ + 2.x and dx/dt = 5, find dy/dt when x = 2.

A: Q.5) If y=x3+2x and dxdt=5 Find: dydt when x=2

Q: From the partial differential eqiuation by eliminating the arbitrary function z=(x2+y2+z2)

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Q: For the slope field shown, which could be a family of anti-derivatives? TUN | 31 1112+\ll || \ ++~…

A: A slope field shows the slope of a differential equation at certain vertical and horizontal…

Q: Find the first partial derivative of w = In(1 + )at (2,0, – 1).

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Q: Form the partial cquatins by eliminating the fiam differential z- Qta) (?+b) atbiliary constant)

A: We have to form the partial differential equations by eliminating the arbitrary constants from…

Q: Find dy/dt at x = 1 and y = x^2 + 3 if dx/dt =

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Q: Find dx dt dx dt at x 2 if y= = - 2x² - 1 and dy dt = - 3.

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Q: A Korean corn dog is a cylindrical piece of hotdog, rice cake, or mozzarella cheese, evenly coated…

A: We will use total derivative to find change  If f is a function of x and y  ∆f=∆x×∂f∂x+∆y×∂f∂y

Q: Find both first partial derivatives. z = 3xVy az ax az ду || ||

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Q: Suppose 4x + 9y - 25, where x and y are functions of t. (a) If dy/dt-, find dx/dt when x = 2 and y =…

A: Given: 4x2+9y2=25 Since, x and y are functions of t, therefore differentiating each sides with…

Q: d²x dx 5 dt2 2- 3x = -9t2 – 1 - - dt dx When t = 0, x = 1, = 0, find x when t = 2 dy %3D -

A: Please see the below picture for detailed solution.

Q: Find dy dy dt at x = z - 1 if y = -5x² + 3 and dx dt 5.

A: topic:- derivatives

Q: but its partial derivatives are not continuous at (0,0).

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Q: Find dx dt dx dt at x = = 2 if y= 2x² - 1 and dy dt - 3.

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Q: Find all the second partial derivatives (including fxy etc.) a) v = sin(2s^2 − t^3)

A: Please see the explanation below

Q: If x3 + y3 = 9 and dx/dt = -3, then what is dy/dt when x = 1 and y = 2?

A: Given,

Q: Can i get help step by step please

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Q: Suppose a particular investor derives utility function - U(x, y) - from owning x units of stocks and…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.