Consider the function g∶Z⟶Z defined by g(n)=n^2+1. Find g(1) and g({1}). Then find g^(-1) (1),g^(-1) (2), and g^(-1) (3).

Q: at point x0=1 ,x1=1 and x2=2 f(x)=sin(x)+(x^2)+xe^2 function crossing second Write down the…

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Q: Find the derivative of by the limit process

A: fx = 342-x

Q: Find the derivative of f(x) = (6x² + 6x – 4)arctan x 12x+6 бх2+бх-4 1 (6x2 + 6x – 4)aretan x…

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Q: Choose the correct answer by using the Product rule of derivative. d dx - (x4.x7) is equal to…

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Q: 2. FIND THE DERIVATIVE BY THE LIMIT PROCESS OF f(x)=x²-6x+5.

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Q: 2. FIND THE DERIVATIVE BY THE LIMIT PROCESS OF f(x)=x³-8x+9.

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Q: f(x) = (6x² - 2x+1)^

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Q: Find anti derivative of    f(x)= (2x2+1)(3x-2)

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Q: By using the second derivative test for functions of two variables, find three positive numbers…

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Q: find the derivative of f(x) = (x²+4)(3x³ – 2x) at the point x = - 3[ use product rule]

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Q: Find the derivative of f (x) = V3x² In(3x²). 2/3x2 A 3x In(3x²) + V3x2 2 + 3x In(3x²) В

A: Given thatfx=3x2ln3x2To find : derivative of…

Q: find the derivative of f(x) = (x²+4)(3x³ - 2x) at the point x = - 3[ use product rule] %3D B.

A: We have to find the derivative

Q: 6. у3 2x – Jx² – 1

A: Given function y=12x-x2-1 we want to derivative of given function with respect to x

Q: Solve the given function using chain rule of differentiation. Show your full solution.

A: On solving this we will get

Q: Find the derivative. using chain rule 7 5. у %3 V1-14x2

A: The given function y=71-14x2

Q: Find the derivative of f(x) = 2² +8-2³ + 5z³. 0 (2) - 1/2 +8-235-24 + 152² O f(2)=1/22-²5 2¹ +152²…

A: The given function is; f(x)=x2/4 +8 - 5x5/3 +5x3.

Q: Determine if the critical points of the function f ( x ) = x³ + x² - x - 2 are maximum or minimum…

A: The given function is: fx=x3+x2-x-2   As we know that; To calculate the critical point, f'x=0.

Q: Find the derivative of the function using Chain Rule. (2x-6)-¹ (x²+3) h(x)=

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Q: Find the derivative of f(x)=8x - 5x+2 using first principles (i.e., use the definition of the…

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Q: Find the derivative of f(x) = (6x² + 6x – 4)arctan x - 1 (бх? + 6х — 4)arctan x(- In(6x2 + 6x – 4) +…

A: Given function is  y=6x2+6x-4arctan x Taking log to each side, we get lny=ln6x2+6x-4arctan x   We…

Q: Find the derivative of f(x) = (1 + 7x2)(x − x2) in two ways. 1. Product Rule 2.Perform the…

A: For product rule we use u=1+7x^2 and v=x-x^2Product rule = u'v+uv'Answer: f'(x)=1-2x+21x^2-28x^3

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: Find the derivative of the function. 4 - 4x – x2 f(x) x2 - 6 — 4х — 2 - -1+ f'(x) = -x – 6

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Q: Find the derivative using the limit process of f(x)=x² + 3x f(x)=x² +3x

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Q: find the derivative of f(x) = (x² +4)(3x³-2x) at the point x =- 3[use product rule]

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Q: Find local maximum or local minimum of f(x) = - sin 2x -x defined on 2'2

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Q: 2 Find the derivative of f(x) =x² – 6 from limit definition. - Show all steps of working. f(x) :…

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Q: Find the derivative of f(x) = V9x8 + 9x (72z + 9)-1/2 (92 + 9x) 1/2(72x + 9) O (928 + 9x)-1/2 -(928…

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Q: Solve for the derivative of the function using chain rule. 9. f(x)= esinx *please explain step by…

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Q: 2) Use the definition of the derivative, f'(x) = lim Ax-0 derivative of f(x) = 5x² + 3. f(x+Ax)-f(x)…

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Q: 1 3. f(x) = (-x4-3)2

A: Solve for the derivative

Q: 2. f(x) = V-3x+ – 2

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Q: Give an example of a function that is defined for all real numbers, is continuous everywhere, but…

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Q: Find the derivative of the function by the limit process. 7 f(x): x - 9

A: Given,          The function is fx=7x-9.

Q: 2- 3x +8 2-X2C

A: Use chain rule to find the derivative. The formula for differentiation is  ddxxn=nxn-1

Q: Provide an example of a function for which it can be shown to have a local maximum at a point using…

A: Firstly, we state both the First Derivative Test and the Second Derivative Test.First Derivative…

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

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Q: equation of the function f whose graph passes thro f'(x) = x/25 - x²

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Q: 5. ƒ(x) = (x²+x−3)√√x²+x=3

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Q: 3. Use the limit definition of a derivative to find f'(x) if f(x) = 3x2 - 5x %3D

A: f(x)=3x2-5x

Q: Find the derivative of f(x) = (5x 2 + 3x + 1) × (3x 2 + 2x − 1) × (x 2 − 1). Show all steps.

A: Given:f(x)=5x2+3x+13x2+2x-1x2-1

Q: In x 9) у - %3D x5

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Q: 4) Use the Limit Definition of a derivative to find f '(3) if f(x): %3D 5-x

A: Given:- f(x) =2/(5-x)  To find:- Use limit Definition of a derivative to find f'(3)

Q: Explain how to find a differential of a function.

A: Let us consider a function f(x) and its differential to be f'(x)

Q: Find the derivative of the function at Po in the direction of A. f(xу) 3 - ху- Зу?, Po(-7,0),…

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Q: In(X+ bnx) %3D

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Q: 4. Find the maxima/minima of f(x) = x³ – x using both 1st and 2nd derivative test.

A: Consider the function: fx=13x3-x. Find maxima, minima.   Find f'x by applying axn'=anxn-1.…

Q: Find 1" and 2nd order partial derivative for the function ax²+by²+2hxy and also verify дхду дудх

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Q: Find the derivative of f(x) = arctan x In(6x² + 6x – 4) 1 1 arctan x 6x2+6x-4

A: Here the given function fx=tan-1x ln6x2+6x-4