Given the functions defined by f(x) = 3x² – 2 and g(x) = x² – 2, calculate the following: (f • g)(-2) -

Q: For the function f(x) = 4x- 3x +2x +6x +2, find f"(x), the third derivative of f, and f''"(x) = %3D

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Q: The derivative of f(x) = 3 (22 + 4x) is - O 3x + 12 O -3x-2(2x + 4) 3x-2(2x + 4) O 3 -3x-3 (2x + 4)

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Q: Given f(x)=−2x^2+4x+13, find f′(−4) using the definition of a derivative.

A: f'(a) = limh→0 f(a+h)-f(a)h.

Q: Find the indicated derivative. 5x2 f'(x) for f(x) = %3D 9x - 4 f'(x) =|

A: We are solving the problem by The by parts rule of derivative.

Q: Find the second derivative of the function.

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Q: Find the derivative of the function f(x) = (5x^4)/12

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Q: For the function f(x)=2x^3-12x^2+20, Use the SECOND DERIVATIVE TEST to find the relative extrema.

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Q: Find the derivative of the function. f(x)=(x^3+3x+9)(8+(1/x^2))

A: The given function f is,

Q: Зах + 3 for x -2

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Q: Find the second derivative of the function. f(x)= (3x³+6)* %D

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Q: find the derivative of f(x) = x2 – 3x + 4, and then 3) evaluate f '(2)

A: Given : f(x) = x² - 3x + 4

Q: Find the second derivative of the function.

A: Given function is  fx=4x32 The derivative used here is  dxndx=nxn-1 The derivative of the first…

Q: Find f'(0) for f(x) x = 0. 0,

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Q: Find the higher-order derivative. f"(x) = 16x³ – ? 34x f'"'(x) = %D

A: To find the third order derivative , we need to differentiate the gives function with respect to x.

Q: Find the third derivative of the given function. f(x) = (3x + 4)³

A: The given function f(x)=3x+43

Q: Find the first, second, and third derivatives of f(x) = x^4 − 2x^3 + 2x^2 − x + 8.

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Q: For the function f(x) = (5x² − 2)4 determine the second derivative in factored form.

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Q: Find the first derivative with respect to the domain variable for the following functions. 6. f (x)…

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Q: Find the derivative of the function. r (x) = 3x 20.6 8. -8 - 6. 6x1.6 2]

A: The derivative of a polynomial function with degree n:

Q: Find f'(x) using the rules for finding derivatives 4x2 - 5x + 2 f(x) = 3x +7

A: We have to find

Q: Find the second and third derivative of the function (a) f(x) = x6 – 3.x5 – 41x – 73 - |

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Q: Use the chain rule to find the derivative of 16 f(x) = 3(8r" - 5z ) * You do not need to expand out…

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Q: For the function f(x) = 5x° - 3x + 2x + 7x + 3, find f"(x), the third derivative of f, and f4) (x),…

A: Third and Fourth derivative of f(x): f3x=300x2-74x+12f4x=600x-74

Q: Given f(x) = -x² – 4x – 6, find f' (4) using the definition of a derivative. Provide your answer…

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Q: function f(x)=2x^3-5x^2+3x+2, find the equation of the tangent line at x=1.

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Q: Consider the following. f(x) = 5x2 + 4x – 18 (a) Find the derivative, by using the definition. f'(x)…

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Q: Given f(x) = –3x² – x + 15, find f' (-3) using the definition of a derivative. Provide your answer…

A: f(x) = -3x2 -x +15 find f-1(-3)

Q: For the function f(x) = 8x^3-2x^2+2x, Find the equation of the tangent line at x = 2.

A: Please see the answer in Step 2

Q: Given f(x) = 5x² + 5x + 2, find f' (x) using the definition of a derivative.

A: Given function is solved through derivative  detailed solution is given below

Q: Find f'(x) using the rules for finding derivatives 4x2 - 7x +6 f(x) = 2x + 1

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Q: The derivative of is f (x) = 3x* + 7x² + 5x + 2 %3D

A: Given, f(x) = 3x4 +7x2 +5x +2

Q: V/2x+3) (x²+1)" 17. f(x)=-

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Q: Find the derivative of the function. f(x) = (x3 + 7x + 5)(3 +1/x2)

A: To determine: Find the derivative of the function.

Q: Find the derivative of the given function. f(x) = (2 - 5x³)-2 1 f'(x) (2– 5x)-2 5x* 3

A: We have to find derivative

Q: For f(x) = (4x – 2)°, find the equation of the tangent line at x = and x = 2. The tangent line at x…

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Q: Given the function: 0 < x < f(x) = 5<x< n 2 п — х

A: Given that f(x)=x,    0&lt;x&lt;π/2π-x,  π/2 &lt;x&lt;πTo the plot the graph and find the fourier…

Q: Given the function F(x)= 1/x2 - Use the definition of the derivative to find f'(2)

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Q: Find the second derivative of the function.   f(x) = x2 + 7x − 4

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Q: For k(x)=(−3x2+2x−3)(x−2)(−x+3), find the derivative of k(x) using the product rule.

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Q: What is f'(x) of the function f(x) = 4xy^3 if you consider y as a constant?

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Q: Determine the 3rd derivative of the given function f(x) = (3x² - 5x + 6)4.

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Q: Find the derivative of the function. f(x) = x2 + 5 − 3x−2

A: Known fact: ddxxn=nxn-1ddxf±g=dfdx±dgdxddxk=0   where k is constant

Q: Find the derivative of the function. g(x) = ((7x^2-4)/(4x+7)^-2

A: We have to find the derivative

Q: For k(x)=(3x+2)(−x+2)(−3x2+x+1), find the derivative of k(x) using the product rule.

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Q: Find the derivative of the function. F(x) = (xª + 7x² – 3)4

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Q: Find the first and second derivatives of the given function. f(x) = 5x3 − 6x2 + 6

A: The given function is f(x) = 5x3 − 6x2 + 6. The derivative of xn is given by: ddxxn=nxn-1 and…

Q: 1. Find the derivative of the following. f(x)=13x* -7x²+5x²+11x+75 a.

A: Formulas:ddx(a f(x))=a ddxf(x)ddx(xn)=an xn-1ddx(a)=0;  where a is a…

Q: Find the derivative of the function f(x) = (2+8)2 8a2+15

A: To find: The derivative of the given function f(x).

Q: Find the second derivative of the function f(x) = 5(2 − 7x)4

A: Find the first derivative as shown below: f'x=ddx52-7x4        =42-7x3ddx2-7x        =5· 42-7x3-7…

Q: Given f(x) = 3x² + 2x. Use the definition of the derivative to show that f'(x) = 6x + 2.

A:

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: