Given the function f(x), whose graph is shown below, place the black draggable dot at the point that corresponds to f^−1(−3).

Q: Find the derivative of f(x) = (3x – 2x?)’using the chain rule %3D

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Q: Let y=sin2x. Differentiate this function without using the chain rule.

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Q: Determine the derivative of the cube root function f(x)=3√x using the limit definition.

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Q: Give a vector valued function whose graph is same as y=ln (x)

A: We know that a function with the representation r→t=ft i∧+gt j∧ is called a vector valued function…

Q: Find the derivative of f(x) = In(x² + 1) %3D

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Q: Use the first principles delta method to find the derivative of y = x2 – x. %3D

A: Here we have to find the derivative of y by using the first principles delta method.

Q: Find the formula for a parabola with its vertex at (9,4) and with a second derivative of -3. f(x)=

A: let's equation of parabola is given by y=ax2+bx+c                                              ..1…

Q: Use implicit differentiation to find y' at (2, 0) for 2x2 + e2ay

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Q: Find the partial derivative. 17zy

A: Given, ∂xe17xy∂x We have to find the partial derivative.

Q: Find y" by implicit differentiation. 3x3 + 4y3 = 2

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Q: Use the limit definition of the partial derivative to verify the formulas

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find the derivative using DELTA METHOD f(x)= 2x-x2

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Q: Find the equation for the perpendicular trajectories of the curve family. 1. x -

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Q: Find all the points on the graph of (x² + y²)² = x² – y² that have horizontal tangent line.

A: Hello. Since your question has multiple parts, we will solve first question for you. If you want…

Q: Sketch the graph of a function z = f(x, y) whose derivative fx is always negative and whose…

A: Given that z=f(x, y) fx is always negativefy is always positive

Q: fx て (X)

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Q: Find the derivative of f(a) %3D 울 -울 + 4VE

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Q: 3 f(x) :

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Q: Use the second derivative to find the location of all local extrema for f (x) = x + x2 – x3, -

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Q: Find the derivative of g(x)= (x+1)/(x+2) using th limit definition.

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Q: Use implicit differentiation to find * at the point (-2,3) on the curve x³ + y³ = 19. %3D

A: Given:- x3+y3 =19 To find:- d2y/dx2

Q: What is the slope of the line tangent to the graph of g(x)=1/x at x=1?

A: Given that ,         g(x)=1x          find slope of tangent at x=1

Q: find all possible functions with the givenderivative. y' = √θ - sec2 θ

A: Given: y'=dydθ=θ-sec2θ for evaluating solution of given differential equation, we use variable…

Q: Use differentials to give an informal justification for the chain rules for derivatives.

A: Consider the given statement. The chain rule of derivatives is defined as. dydx=dydududx Let's take…

Q: Analyze the stationary points of f(x) = x2ex by applying the second-order derivative test.

A: Stationary points are occurred where the first derivative of the function becomes zero. If the Value…

Q: How can the derivative function definition be applied to this problem?

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Q: Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.

A: Consider the given: The numerical derivative does not exist a point in three cases: 1) when there is…

Q: Suppose that the first derivative of y = ƒ(x) is y' = 6(x + 1)(x - 2)2. At what points, if any, does…

A: Given the first derivative is: y'=6x+1x-22

Q: Find the derivative and simplify exy -x² = 4Y² %3D

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Q: Estimate the derivative of the function f (x) = -3 at the point a = 3. %3D

A: Here given as fx=x3-3 Differentiate with respect to x f'x=ddxx3-3=ddxx3-ddx3=13

Q: Find The derivaTive of f(X) = -x²+ 3X + 2 Using the de finiTion of the derivative

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Q: What

A: The correct option is (B).

Q: What is the gradient of the curve y = x^3+4x^2-6x+3   at the point where x=-2 ?

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Q: Q4/ Explain the rule of maximum and minimum using Derivatives with an еxample?

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Q: Find the derivative using the long method 3-t to

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Q: 1 m' (x) = x In(x)

A: Given: m'x=1xlnx for finding anti-derivative of given expression, we substitute lnx=u…

Q: Find y" by implicit differentiation. 5x3 + 4y3 = 9 У" - %3D

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Q: Sketch the graph of y= x²+ - by using the properties of the derivative. 2

A: To sketch the graph

Q: Find the point on the line y 2 x-3 that is nearest to tne ofigin.

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Q: Find the gradient of the curve y = x° – x2 – 8x – 2 at the point on - - - the curve whose…

A: As we know that; The expression for the gradient or slope; m=dydx And The Power law; ddxxn=nxn-1

Q: Draw the function x = 2y-y2 by using the tools of derivatives?

A: The given function isx=2y-y2.

Q: Find the point on the parabola y= X- + 4 whose tangent line is parallel with y = 3x -5

A: Let a point on the parabola is h,k. Now the slope of the tangent line is given by: m=dydxh,k Since,…

Q: Compute the derivative of f(x) = arcsin(x² e3=).

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Q: A company has identified that the revenue R for a particular product is given by the equation R(x)…

A: The given Revenue function R(x)=23x3-40x2-450x.  Task: To maximize this revenue function.

Q: Find y'' by implicit differentiation 4x3+3y3=6

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Q: Find the derivative of the function f(x) = v4-x2 by definition

A: The given function is f(x)=4-x2 The definition of the derivative is given by: If a function f(x) is…

Q: Describe how you would use the second derivative to determine a local minimum or maximum.

A: Given data is: How you would use the second derivative to determine a local minimum or maximum

Q: Suppose that the first derivative of y = ƒ(x) is y′ = 6(x + 1)(x - 2)2. At what points, if any, does…

A: To determine if the function has any points of maxima, minima or inflection, use second derivative…

Q: Suppose that the first derivative of y = ƒ(x) is y′ = 6x(x + 1)(x - 2). At what points, if any, does…

A: Here the first derivative of the given function is y’= 6 x (x+1) (x-2). If a function has zero…

Q: Compute the derivative of f (x) : = arcsin(x² e³«).

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