Suppose that z = f(x, y) is differentiable at the point (1024, 64) withf, (1024, 64) = 4 and f, (1024, 64) = -2. If.x = r and %3D dz when t = 4. dt y = t, find- dz| %3D dt

Q: dx 1s+ kıl35-x) +kaly-x) dy %3D dt k, , k. k3 are Con Stants.

A: Given system is dxdt=15+k135-x+k2y-xdydt=k2x-y+k335-y Here, 1k1=5⇒k1=151k2=10⇒k2=1101k3=5⇒k3=15 So,…

Q: Suppose that z is a differentiable function of x and y with dz (2, 5) = 108 and- dx dz (2, 5) = 9.…

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Q: Assume that x and y are functions of t. If y = x² + 4x and dx/dt = 4, find dy/dt when x = 1. dy dt…

A: Solve the following

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A: Find dz/st when t=3

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

A: To find the value of dy/dt in first case and value of dx/dt in second case.

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

A: We can use application of derivative in order to solve the given problem.

Q: Assume that x and y are both differentiable functions of t. Find dy/dt when x = 16 and dx/dt = 9 for…

A: Solution is given below:

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

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Q: Suppose that z = f(x, y) is differentiable at the point (1024, 256) withf(1024, 256) = 2 and f,…

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Q: Let z = f(x,y)= x^3+ xy+ y^4    (a)  Use differentials to estimate Δz as x changes from 1 to 1.05…

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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: Differentiate both side:-

Q: Find dw/ds and aw/at using the appropriate Chain Rule. Function Point w = sin(5x + 6y) X = s + t, y…

A: According to guidelines we solve only first three parts.

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

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Q: Suppose f(x, y) =                             ((xy2) / (x2 + y4)), for (x, y) ≠ (0, 0)…

A: The given function is,

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

A: Given :  x 2 + y 2 = 169  Find dx / dt and dy / dt

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A: Given If x, y, and z are lengths of the edges of a rectangular box

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Q: If a and ß are positive constants, show that the particular solution of dy %3D У (В — ау) dt that…

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Q: Q5. If W = x² y + 2xyz , x = t², y = t + 1, z = 2t at t = 1. Find the total differential

A: Let's find.

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: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(5) = 8, g'(5) = 9, h(5)…

A: Given that z=fx,y, where f is differentiable. Here, x=gt and y=ht. Also, let, g5=8, g'5=9, h5=-7,…

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

A: Given   xy=4

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

A: Given function is Differentiating with respect to t, we get

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

A:

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

A: This question is related to implicit differentiation, We will solve it using given information.

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: Suppose z = f(x, y), where f is differentiable, x = g(t), and y = h(t). If g(4) = – 4, g'(4) = 9,…

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Q: Suppose x(t) and y(t) satisfy da = y? – 1 , dt dy = 2 – 2x. dt - - d (3x2 – 6x 0. + y³ – 3y) = Show…

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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 function is y=2x2-3x. (a)To find dydt when x=4 and dxdt=1. Differentiating the given function…

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

A: partial differentiation

Q: Suppose y = V 2x + 1, where x and y are functions of t. %3D (a) If dx/dt = 9, find dy/dt when x = 4.…

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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: We can solve this as follows:

Q: Assume w = x²y*, where x and y are functions of t. Find dw/dt whenx = 3, dx/dt = 2, dy/dt = 4 and y…

A: To find the derivative of the given function w,  we need to apply chain rule of differentiation and…

Q: if (2,y) # (0,0) Let f(x, y) = aª + yª Show that D1f(0,0) and if (2,y) = (0,0) D2f(0,0) exist but f…

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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:

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

A: Differentiate both sides with respect to t and form an equation.

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

A: Given query is to find the derivative of x and y with respect to t.

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

A:

Q: assume x and y are functions of t.  Evaluate dy/dt for the following: y3=2x4+6; dx/dt=2, x=1, y=2

A: The given function is  y3 = 2x4 + 6    ...... (1) dx/dt = 2, x = 1,   y = 2

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

A: Given xy=6, we need to find values of dx/dt and dy/dt under given conditions. The solution is given…

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

A: (a) Differentiate the functions w.r.t t, ddtx2+y2=100 2xdxdt+2ydydt=0 Substitute the given values,

Q: Suppose x, y, and z are positive functions of t. If z x + y?, dx/dt 1, and dy/dt 2, find dz/dt when…

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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,            xy=2

Q: If z = e2x+ 3y and x = In t, y = t2, calculate dz from the total dt derivative formula and show that…

A:

Q: Assume x and y are functions of t. Evaluate dy over dt for the following. y = 2x 2 + 6 ; dx over dt…

A: