Given the equation y In (x? + y² + 4) = 4, evaluate dy Assume that the equation implicitly defines y as a differentiable function of x. xp If F(x.y) = y In (x? + y² + 4) - 4, then F, %3D If F(x,y) = y In (x +y² + 4) - 4, then F, = dx

Q: Suppose y = v2x + 1, where x and y are functions of t. dx = 9, find dt dy (а) If when x = 4. dt dy…

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Q: 2. Show that the function u = p(xy) + Vry v(y/x) provides the equation = 0. dy? | dx²

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Q: Supose z is implicitly dofimed by the equation qy+ 3x + XyZ + 32=9 in an onvanment of the point…

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Q: find f given f (z, y) = e + 2ry 4y at (0,3)

A: Topic- partial differential

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Q: dy Given the equation y In (x* +y +1) = 4, evaluate . Assume that the equation implicitly defines y…

A: The given equation is; y ln(x4 +y2 +1)=4 And F(x,y) = y ln(x4 +y2 +1) - 4

Q: 2. Show that the function u = e(xy) + VrY 4(y/x) provides the equation Pu = 0. dy? %3D -

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Q: Does the given equation F(y; x) = x° - 2a²y+ 3xy- 22 0 define an implicit function around the point…

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Q: Let f (x, y) = xy2 + 5. Evaluate df/dy at (x, y) = (2, -1) and interpret your result.

A: Given: f (x, y) = xy2 + 5.

Q: If z = f(x, y), where f is differentiable, and g(t) g(3) = 2 g'(3) = -3 fx(2, -8) = 9 X = h(t) y…

A: Given,           z=fx,y, where f is differentiable, and                x=gt    and    y=ht…

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A: We have to find the Linear approximation of the given function.

Q: Given f(x, y) = 3æ'y- 8ry. Compute: www dy?

A: This question can be solved using the concept of partial derivatives.

Q: Suppose that u and v are differentiable at x = 2 and that u(2) = 4, v(2) = -9, u'(2) = 5, and v'(2)…

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A: A multivariable function is a rule that connects two or more variables. The partial derivative of a…

Q: Suppose y = v2x + 1, where x and y are functions of t. dx = 6, find dt dy when x = 4. dt (a) If dy…

A: Given y=2x+1 dydx=dydtdxdt

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A: By using partial differentiation .

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Q: dy Assuming 8x³ - 10y² - 2xy = 0 defines y as a differentiable function of x, use the theorem dx dx…

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Q: find given f (x, y) = eª + 2xy² – 4y at (0, 3) af dy'

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Q: If y = f(x) is the solution of (5aty – 12a – 2y³)dx + (x³ + 4y³ – 6xy?)dy = 0, f(0) = 0, then

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Q: If the equation x²e+z_224cos(x-224z)=n?e+224 defines z implicitly as a differentiable function of x…

A: Since you have asked multiple questions, we will solve the first question for you. The other…

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A: Given: fx,y=ex2ln5xy. To find: ∂2f∂y2 Solution: In partial derivative we differentiate with respect…

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A: The given problem is to find the third degree taylor polynomial of given function f(x,y) about point…

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A: We have to solve integral

Q: Assuming 9x° – 5y - 4xy = 0 defines y as a differentiable function of x, use the theorem dx - to…

A: Given: 9x3-5y2-4xy=0 We have to calculate dydx(1,1) by the given formula.

Q: find given f (x, y) = e² + 2xy² – 4y at (0,3) af dy'

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Q: If y = x(x – 1)* then y' at z = 2 is equal to

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Q: Let x and y be differentiable functions of t, and let s = /4x + 6y be a function of x and y. Answer…

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Q: If the equation x?ev+z_184cos(x-184z)=²e+184 defines z implicitly as a differentiable function of x…

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Q: dy Assuming 3x +y-4xy 0 defines y as a differentiable function of x, use the theorem Fx to find Fy…

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Q: 6. If y is a differentiable function of r and 24 + 2y5³ 5y2, then find - dy da

A: The given equation is x4+2y5x3=5y2

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Q: Consider the function y defined implicitly by 3(x2 + y2)? = 100xy. Use the linear approximation at…

A: Given : 3(x² + y²) = 100xy

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: Solve the following problem dw dw + x dt 1, -00 0, %3D dx with w(x, 0) = f(x).

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Q: ex+y+Z If f(x, y) = x+ey+e²> then the %3D ex+eY +eZ > value of fx + fy + fz is equal 2f f

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Q: Suppose X has pdt f(x) = - z(1 +x) which one is the pdf for Y 2X. (A) f)D- (8) f0)=- z(l + 4y) (4 +…

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Q: 4. Suppose that c is a constant and that u is a continuous, differentiable function of x. Show:…

A: prove of the above question is given below...

Q: Given the eguation y In (x +y + 1) = 8, evaluate dy Assume that the equation implicitly defines y as…

A: Differentiate with respect to x

Q: of Find of and for the following function. ду 1(x,y) = (2x – 9y)5 %3D of 1 дх of 1 dy

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Q: Given f(x, y) = - (4x°y + xy® ). Compute: dy?

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Q: Given the equation y In (x+y" +9) = 5, evaluate dy Assume that the equation implicitly defines y as…

A: The given equation is  y.ln(x3 + y4 +9) = 5 To find dy/dx

Q: Q1. Solve the follounig ordinary diflerential agethins, 2 ci) dy ;If yoo when x=0 = xe dx dy + Cot y…

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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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Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: