dz Suppose that z = f(x, y) is differentiable at the point (8, 16) with f,(8, 16) = 3 and f, (8, 16) = -7. If.x = ° and y = f, find- dt when t = 2. dz| dt =2

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A: topic- partial differentiation

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Q: Find fr and fy- S(x, y) = /"9e" dt f.(r, y) : %3D f,(x, y) =

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Q: 4. If f(x, y, z) derivative of f at (1,3,0), in the direction of i = i+ 2j – k. = x sin yz, (a) find…

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Q: Assume that x=x(t) and y=y(t). Let y=x^2 +1 and dx/dt =5 when x=4 Find dy/dt when x=4 dy/dt=

A: Simply take the derivative and put the given value and simplify.

Q: Assume that x = x(t) and y=y(t). Let y = x³ +5 and dt Find dt dy dt when x = 3. (Simplify your…

A: Here is the solution:

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Q: = y – 2², dt dy = y - ar. - у — dt For parameter a, classify the equilibrium points when a>5

A: Both the equilibrium points (0, 0) and (a, a2) are saddles.   Explanation: Let   First, we find the…

Q: A particle moves in a plane according to -t, x = (t+1)e; y=2tet -t Determine the simplified…

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Q: Use the Chain Rule to find dz/dt. z = sqrt 3+ x^2+y^2, x= 3 ln t, y= cos t

A: Use chain rule to differentiate z

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Q: (3) Consider the derivative dz = 2xydx + (x² + 2y)dy Evaluate whether this is a total derivative, by…

A: We will check whether the given function is total derivative or not. We also integrate dz pathwise.

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Q: Find the first partial derivatives with respect to x, y, and z. Ex, y, 2) = 3x?y - 6xyz + Byz? ,(X,…

A: We have to solve this problem by partial derivative method.

Q: The temperature at any point (x, y) in a steel plate is T = 500o - 0.5x2 - 1.2y2, where x and y are…

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

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Q: Solve dy = ytan t, dt using separation of variables given the inital condition y(0) = 15. Assume the…

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: Given : Equation x2 + y2 = 25 and x and y both differentiable functions of t.   To find : (a)…

Q: В. Find dz/əx , əz/əy at the point (1,1,1) if x³ + z² + ye*z + xz cos y = 0 .

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Q: Find dy/dt. Show all work. y= t^3(t^3+2)^6

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Q: Suppose that the temperature in a given region is given by T(x,y)=200xy(1-x2-2y2) . Suppose that you…

A: Given that,Temperature in a given region is given byTx, y=200xy1-x2-2y2You and your friend are at…

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Q: * If z = f (x, y); then its total differential can be expressed as дz dydz date - ( 7 ), v + ( ;) -…

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Q: If y is a function of t and z= 4y²+y• find dz/ dt when y=2 and dy/ dt = – 1 %3D

A: z=4y2+y, dy/dt=-1

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A: We need to find maximum rate of change.

Q: Find dw/ds and dw/at using the appropriate Chain Rule. Function Values w = y - 5x²y x = e°, y = e S…

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Q: Q4) If Z-y , Determine the first order partial derivative (w.r.t, x) and (w.r.t, y)

A: To find: The first order partial derivative of Z=yx2 with respect to x and y. Concept used: The…

Q: 3x The directional derivative of f(x,y,z)=ln at the point P (2,0,-1) in the direction 1+yz z² from P…

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Q: dz Use the Chain Rule to find dt for z = x? + y? + xy, x = sin t, y = et.

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Q: b) Use the chain rule for partial derivative to find 2 when z = f(x, y) = x²y + ln(x + y) and (x, y)…

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Q: Find the differential of f(x, y) = 3+y² at the point (2, 3). df: ((3x^2)dx+(2y)dy)/(2sqrt(x^3+y^2))…

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Q: A heat-seeking particle is located at the point (2, −2) on a metal plate whose temperature at (x,y)…

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Q: Use the Chain Rule to find dz/dt.z = sqt(8+x^2+y^2,    x = 4 ln t,    y = cos t dz/dt=

A: Please refer to the image below

Q: A particle is moving along the curve y=x- 2 where x and y are functions of t. Find dx/dt if dy/dt =…

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Q: Find the value of dx at the point (1,1,1) if the equation 6xy + z"x-2yz = 5 defines z as a function…

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Q: 8. Find the directional derivative of f (x, y, z) = xy²z³ at P(2,1,1) in the direction of Q(0, –3,5)

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Q: dg Use the Chain Rule to evaluate the partial derivative at the point (r, 0) = (2/2, 7 where g(x, y)…

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Q: Find the maximum rate of change in f (x, y, z) = tan(r + 2y + 3z) at P = (-5,1,1).

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Q: 2. Find the directional derivative of f(x, y, z) = y – Væ² + z² at P(-3,1,4) in the direction of a =…

A: Given f(x,y,z)=y-x2+z2

Q: Assume that z and y are both differentiable functions of t and are related by the equation y = cos…

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Q: Find the directional derivative of f(x, y, z) = 5y at P(5, 1, –4) x + z in the direction from P to…

A: We have to find directional derivatives for the given function.

Q: Find fr and fy- f(x, y) = fetlo dt f.(r, y) = fy(x, y)

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Q: 4. If f(x, y, z) = x sin yz, (a) find the gradient of f and (b) find the directional derivative of f…

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