Assuming that the equation below defines y as a differentiable function of x, find the value of dy / dx at the given point. 3x? + xy + 4y? - 96 = 0, (4,3)

Q: Use implicit differentiation to find y for the equation below land évaluate y' ăt the inochicated…

A: An implicit function is a function described in terms of both dependepent and independent variables,…

Q: Assuming that the equation below defines y as a differentiable function of x, find the value of dy /…

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Q: Answer the question below: The student should find the local linear approximation of a function in…

A: Let's find.

Q: dy and 2xy + 2. Find the expression for Assume that y is defined implicitly as a function of x by…

A: We differentiate both sides with respect to x. Use product rule for 2xy Then solve for dy/dx.

Q: Using the properties of derivatives, solve for the following, do not oversimplify your answer. g(t)…

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Q: Find the derivative of the function at Po in the direction of u. X-y g(x.y) = xy +3' Po(2, - 2), u=…

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Q: Find dy/dx by implicit differentiation. x2 - 8xy + y2 = 8 y' = Need Help? Read It Watch It Talk to a…

A: To find the derivative of function implicitly.

Q: = 1. Let y? + y = x. Using implicit Suppose that y(x) is a function and that y(2) differentian find…

A: Given  y2+y=x y2=1 To find : y'2 and equation of tangent to y(x) at x=2.

Q: Assuming - 10x³ – 8y? - 2xy = 0 defines y as a differentiable function of x, use the theorem Fx to…

A: We need to find dy/dx at the point (-1,-1)

Q: In what direction is the derivative of f(x,y)=xy+y2 at ​P(5​,9​) equal to​ zero?

A: Option A is correct. Find the derivative of f(x,y) in the direction at P(5,9).

Q: Find the derivative of the function at Po in the direction of u. x-y g(x,y) = 3. ху +3° Po(-1,2), u=…

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Q: erential equation: an y = x2. If y(0) e value (corrected up fy(1)?

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Q: A. . Find the derivative of the function at Po in direction of A. g(x,y) = x- + V3sec (2xy), Po (1,…

A: We know that; The expression for the directional derivative of the function g in the direction of A…

Q: Find the derivative of the function. y= 2x°e* Which of the following shows how to find the…

A: Topic :- Derivative Correct option :- D

Q: I. The Derivatives: Perform long method. 1. v = Ja2 – y? 2. x = 3t2 - 2 Vt

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Q: a)x^2 + y^3 =2xy^2 Give the function for dy /dx.   Give the equation of the tangent line at the…

A: our objective is to find the derivative and tangent line

Q: 1. The point P(p, 1), where p > 0, lies on the curve x² + 2xy³ – 3yt = 0. a) Calculate the value of…

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Q: dx for y - 2x3 - 3х + 1. Determine the derivative a. 6x - 3 b. 6x – 3x 3x -3 d. x-3 с. а.

A: In the first question we have to differentiate y w.r.t x In second question we have to calculate the…

Q: Find the particular solution of the differential equation

A: The given D.E. is the first order separable O.D.E.Rearrange the given D.E.

Q: Assuming that the equation below defines y as a differentiable function of x, find the value of dy /…

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Q: Find the derivative of the function at Po in the direction of u. x-y g(x.y)= Зху +2" Po(-1,1), u=…

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Q: dy Find when 2x? + 3x°y – 3y3 = 32. dx dy dx The slope of the tangent line to this curve at the…

A: Take the derivative with respect to x using chain rule of derivative.

Q: (a) If x2 + y2 = 100, find dx (b) Find an equation of the tangent to the circle x² + y² = 100 at the…

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Q: dy Find when 5x? + 3x°y – 5y3 = 28. - dx dy dx The slope of the tangent line to this curve at the…

A: Given,  5x2+3x3y-5y3=28

Q: Find the slope of the graph of the equation at the given point. (If an answer is undefined, enter…

A: we have been given the slope of the equation xy=x-2y,at (4,1) it can be written as  xy=x-2y

Q: Find the derivative of the function at Po in the direction of A. f(x,у) - 4хy + 3у?, Po(-1,1), А-D6і…

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Q: In what directions is the derivative of f(x,y) = xy +y at P(7,6) equal to zero? .. Select the…

A: We have to solve the problem

Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the…

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Q: Z=- 1+x? 2 ; d²z/dx? Y = (3x3 + 2)4 ;y" Y = V(2x + 1)2 yiv %3D

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Q: Using Numerical Values 39, Suppose u and v are finctions of x that are differentiable atx=0 and that…

A: Since you have asked a question with multiple sub parts, we will solve the first sub parts for you…

Q: Use implicit differentiation to find y' and then evaluate y' at (- 2,0). - 32 ey = x5 - y3 y' = D…

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Q: dy d {-3xy} in terms of x , y , and dx y is a differentiable function of x . Write dx

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Q: Assuming that the equation below defines y as a differentiable function of x, find the value of…

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Q: Find the first derivative of y with respect to x (y') of the given function.

A: Given function is  : x2y-xy2+x2+y2=0

Q: differntiate  y=ax^2 +bx+r   Find an equation for the tangent line to the curve at the given…

A: Topic:- Differentiation

Q: # 16 Find the derivative y' of the equation x3 + y3 = 3xy, the Folium of Descartes. ソーズ アーズ %3D (A)…

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Q: Determine if the equation (x* +y°) dx + (5xy* +y°) dy = 0 is exact. Identify M = and N = ƏM ƏN The…

A: For differential equation ,M dx + N dy=0 is to be exact if∂M∂y=∂N∂xthen solution is∫ M dx + ∫ N…

Q: Find the derivative of the function at Po in the direction of A. f(x.y.z) = xy + yz + zx, (3, - 3, -…

A: Given: fx,y,z=xy+yz+zx, Po3,-3,-2, A=9i+6j-2k

Q: Find the derivative of the function at Po in the direction of u. g(x,y)= 3x-y 5xy +9¹ Po(2,-1), u5i…

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Q: Find the directions in which the function increases and decreases most rapidly at Po. Then find the…

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Q: 24. Find the second derivative of y =. b. d. 25. Find the derivative of y with respect to x of the…

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Q: d?y Find the curve, y that satisfies the conditions %3D dx2 = 6x; the line y = 5 - 3x is (b) tangent…

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Q: Use implicit differentiation to find y' and then evaluate y' at (2,0). 4 eY = x? - y³ y' = D y'l20)…

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Q: (a) Find the first and second derivatives of the following function (1² + x)(x² – x + 1) f(x) = %3D…

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Q: Find the indicated derivative. In this case, the independent variable is a (unspecified)…

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Q: d'y or the function y = 8 e" the second order derivative is %3D - - dx? -3 O 8e" + 12x -2 O 8e" + 6x…

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Q: Question Given s(x) = 7x + 4x + x -2, find s' (x) using the definition of a derivative. (Do not…

A: Given query is to find the derivative using bg definition.

Q: z+7 at the point (0, - (0.-) Find the equation of the tangent line to the graph of the function f(z)…

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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.