the derivative of f(x) = (2+ 3x)² (5x² – 3)ž

Q: x³+3x f(x) = 2-4x+3

A: Given that fx=x3+3xx2-4x+3   Quotient rule for differentiation. ddxuv=v·ddxu-uddxvv2 Here,  u=x3+3x,…

Q: finding the local mins and maximums and the intervals of increase and decrease and making a sign…

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Q: [CLO-2] Find the derivative of f (x) = x −x5 e 2x + 3 1-5x4 x-x5 x-5x5 2/x −x5 1-5x4 Vx-x5 −5x4…

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Q: Using high-accuracy central difference formula, determine the derivative of the function F(x) =…

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Q: Using the second derivative test, find the local extrema of the function f(x)=x3−9x2+24x−7.

A: We find the first and the second derivative using the power rule

Q: Find the derivative of the function using the definition of derivative. State the domain of the…

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Q: function D = x* - 18x + 12 a derivative of ) = 4x – 36x = 4x(x? – 9) - 9) |

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Q: Derivative. The derivative of e-3 h(x) e(3x2 + 13) 4 + is none of the other answers e-3(-3)(4 +…

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Q: f(x)= (3x²+2x+1)

A: Topic = Derivative

Q: Finding the Derivative by the Limit Process InExercises 1–4, find the derivative of the function by…

A: Given function is: f(x) = 12 We have to find the derivative of f(x) using the limit process.

Q: Ths function f(x) has derivative f'(x) given by x(x² – 4) (4 – x)(x² + 9) f'(x) = Solve the…

A: we have f'(x)=x(x2-4)(4-x)(x2+9)

Q: y = 1.2889x3 - 358.53x2 + 48536x - 34188 What is the second derivative, what is the point of…

A: we have been given an equation  y=1.2889x3-358.53x2+48536x-34188 to find the inflection point we…

Q: Finding the Slope of a Tangent Line InExercises 9–14, find the slope of the tangent line tothe graph…

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Q: The graph of the function f(x) = x³ – 3x has one local maximum and one local minimum point. Find…

A: Given function is: fx=x3-3x

Q: find the derivative of f(x)=2x2-3x from first principles

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Q: (b) f(x) = (3x – 2a²)³

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Q: (5x²+4)

A: ddx15x2+43

Q: f(x) = 2x-3/4

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Q: f(x)= (4x² +8x+2)

A: We can find the derivative using chain rule as below.

Q: Finding the derivative of f(x) = 2x2+3x-1, using definition of derivative %3D A- В BIB:

A: Our objective is to find the derivative of f(x) using definition.

Q: f(x)=√√3x² +6x+2

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Q: explain

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Q: Higher-order derivatives Find ƒ′(x), ƒ″(x), and ƒ‴(x) for thefollowing functions. ƒ(x) = 3x3 + 5x2 +…

A: the given function is: f(x)=3x3+5x2+6x we have to find f'(x), f''(x) and f'''(x).

Q: First and second derivatives Find ƒ′(x) and ƒ″(x).

A: Given, To find f'(x)=? f''(x)=?

Q: 5. (5 points) Use derivative rules to find the derivative of f(x)=2+9x-7x° .

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Q: Deduction of the second derivative criterion for optimization of functions of two variables using…

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Q: derivative of f(x)=\sqrt(x)(1-x-x^(2))

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: finding the local mins and maximums and the intervals of increase and decrease and making a sign…

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Q: f(x+Ax)-f(x) Use the definition of the derivative f'(x) = lim Ax-0 to find the equation of the line…

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Q: Combining derivative rules Find the derivative of

A: Recall quotient rule ddxmn=mddxn+nddxm…

Q: A function has the derivative f'(x) = 3x2 - 7x + 2. What are the stationary points of f, and their…

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Q: Using the limit definition of a derivative find the derivative of f(x)= the square root of 4x-3.…

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Q: Using "Numerical Differentiation (Central Finite Difference)" Problem Solving f(x) = 4e-2xsin(x2)…

A: 1. The product rule for differentiation states that ddx[f(x)·g(x)]=g(x)f'(x)+f(x)g'(x), where f(x)…

Q: Solve the problem using derivative and indeterminate forms. Show complete and detailed solution

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Q: using the first derivative test, determine the relative extrema of the function f(x)=…

A: Given query is to find the extrimas for the function.

Q: Find the derivative of the function using the definition of derivative. g(x) = square root of (9-x)…

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Q: Test for relative maxima and minima. Use the second-derivative test, if possible. y = x3 - 12x +3

A: Given  y=x3-12x+3 The the first derivative is y'=3x2-12 The critical points are those points at…

Q: g(x)=(2x-x3) h(x)=(8x+5) f(x)=(2x-x3)(8x-5) Find g1(X) and find h1(X) Use product rule to find…

A: Given functions are:

Q: -9) √(x+2)]2

A: The function given is , fx=x2-9x+22. To find the derivative of the function, Apply the product rule,…

Q: Using the First Derivative Test, what are the local extrema for the function g(x) - + 9x- 28x + 1?…

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Q: Computing a derivative Consider once again the function f(x) = -16x 2 + 96x

A: Computing a derivative Consider once again the function f(x) = -16x 2 + 96x

Q: Function:  f(x) = x/(x2-1)   Use the second derivative to discuss concavity. The second derivative…

A: Given, f(x)=xx2-1we have to use the second derivaive test to discuss concavity.the second derivative…

Q: y = 1.2889x3 - 358.53x2 + 48536x - 34188 What is the second derivative, what is the point of…

A: First we need to find inflection point:

Q: Solve the problems using indeterminate form and derivativ

A: Given that:                  1.limx→0πx-12x2+πx(e2πx-1)2.limx→∞4+x2x

Q: 19-29 Find the derivative of the function using the definition of derivative. State the domain of…

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Q: Find the slope of the graph of the function f(x) = /2x at (2,2). Then find an equation of the line…

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Q: An open box is to be made out of a 12-inch by 14-inch piece of cardboard by cutting out squares of…

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Q: Derivative 2. Use the chain rule to find the derivative of f(x) = (3x² – 9)-4

A: Given: