Find the maximum rate of change of f at the given point and the direction in which it occurs. F(x, y) = 2y²/x, maximum rate of change direction

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A: Leibnitz integral rule.

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A: Since you have posted multiple questions i can do first question as per our company guidelines…

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Q: Describe the change in accuracy of dz as an approximation of ∆z as ∆x and ∆y increase.

A: Given , z=fx,yWe do dz using the partial derivates zx & zy .So , dz=zx.dx & zy.dywhere zx…

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Q: Find the derivative, dy / dx, at the points where x = 1 on the folium                    (x 2 + y 2)…

A: given,       (x 2 + y 2) 2 = (25/4) x y 2 .

Q: Use the limit definition of the derivative to find the instantaneous rate of change of f(r) = V9r +…

A: Given:       fx=9x+5 at x=1  Instantaneous rate of change :    If y=fx, the instantaneous rate of…

Q: Find the derivative of the function y = 5 . 5t +3·3. dy dt

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Q: Given that x and y are functions of time, find the indicated rate of change. dx when x 6, y = 3, and…

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Q: Find maximum rate of change of f at the given point. f(x,y)=sin(xy), (1,0)

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Q: Find the derivative of the function. 2x F(x) = arctan(t) dt Vx F'(x) : %D

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Q: A point moves along the parabola y = x² in such a way that the rate of change of x : kx, || dx dt…

A: Since dx/dt = 10 at x = 5, therefore 10 = 5k k = 2 Now, calculate dx/dt at x = 7. dx/dt|x=7 = 2*7 =…

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Q: Find the average rate of change of f(x) = x2 + 3x + 1from 1 to 2. Use this result to find the…

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Q: Find the derivative of the function.

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Q: What is the average rate of change of the function g(t) over the interval from t = a to t = b? How…

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Q: Find the derivative of the function. -1 y = (3t – 1)(6t – 5) dy dt II

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Q: 5. Find the rate of change of the distance D between the origin and a moving point on the graph dx…

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Q: Can i get help step by step please

A: We have to use the formula: with a=11

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Q: Evaluate the derivative of the function r(t)=⟨sin2t,cost,2sect⟩ at t=π6.

A: To find the derivative of the given function.

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Q: Suppose that a company can produce 12,000 units when the number of hours of skilled labor y and…

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Q: The average rate of change of the function y = sinx over the interval [0, ]is 4

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Q: Find the instantaneous rate of change of y =- at x = a

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Q: Find dy/dx. Find the gradient of the tangent that touches the graph at x = 2.

A: Given function - y = ln(9x+4) + ex25 + 8-2xDifferentiating on both sides with respect to x - dydx =…

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Q: at is the maximum rate of change of f (x, y,z) at P?

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Q: Find the derivative of f(x, y) = (2x – y°, sin(ry), r²y*)

A: Given f(x,y)=2x-y3,sin(xy),x2y3 differentiate f(x , y) with respect to x we get…

Q: b) y = vs3 + 1 dy dt

A: We used the chain rule.

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Q: Let m(x) be the slope of the tangent line to the curve y = 2x³-6x² + 3x at the point (x, y). Find…

A: Given: y=2x3-6x2+3x

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Q: Find the derivative of y with respect to x.   Y=lnx /3+2ln x   dy/dx=___________

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Q: The total derivative of the function f(x, y) =3x'y- xy is

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Q: DETERMINE THE INSTANTANEOUS RATE OF CHANGE OF THE FUNCTION AT X=1 sin (2³) 1 + √t - f(x) = x3 dt

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