The acceleration of a moving body is given by the function a = 6t +4. If the velocity after 4 seconds is 70 m/s and the distance moved (displacement) in that time is 140 m, determine: (a) The function which represents the velocity of the body. (b) The function which represents the displacement of the body.

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A: We use the power rule and chain rule.

Q: Find the indicated derivative. 3 If f(x) = 24³x² + 96 3 VX find f'(8).

A: Here we will find f'(8),

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A: Given,           The function is fx=2x3-8x2+76.

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Q: solve for first and second derivative (x2 + 8)2(x − 8)

A: Let

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A:

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

A:

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A: Given: f""(x)=(x^2+9)^2

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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: solve for the first and second derivative of the function:

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A: Given function: y=29-x24

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

A:

Q: Write a derivative formula for the function fx)- 12.2(4.7 x2 1.5475x(4.7-2( 4.7*) f'(x) 12.2 = X

A: Given

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Q: iven the function y=2x³-4x²+5,

A: Given, the function               y=2x3-4x2+5

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Q: Find the derivative. a) (x-3)(x+2)(x^3) b) 9x^2(10x+4)

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Q: Find the first and second derivatives of the function. (6t2 - 4)2 (5t2)

A: Given function: f(t) = (6t2 - 4)2 (5t2) = (36t4 - 48t2 + 16) (5t2) = 180t6 - 240t4 + 80t2 Recall the…

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A: Solution:Given        f(x)=3x2-4   at (1,-2)To find:Slope of the line tangent to the graph The…

Q: Find the second derivative of the function. f(x)= [3x3+7]7

A:

Q: Find the slope of the line tangent to the graph of the function defined by f(x) = x2 – 3x + 4 at…

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Q: the derivative () of = f(x) = 2

A: Please refer to the image below

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Q: Find the derivative of the function. f(x) =  x3 − 4 x2 + 2

A:

Q: Find the derivative of the function. F(x) = (x4 + 5x2 – 9)6

A:

Q: Given f(x)= x^2 + 7x, find the average rate of change of f(x) on the interval |-3,-3+h| . Answer…

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Q: -y = a(10z² –8z+7)

A: Using composite derivative formula.

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A: Find the second derivative of the function f(x) = 8/(x − 2)2

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A: We have to find the 1st,2nd,and 3rd derivative of the given function.

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A: The objective of the question is determine the derivative of the given function.

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Q: 13: 3. y = V(4x + 3)3

A:

Q: Find the second derivative of the function. f(x) = 8(2 − 2x)4 f"(x)=

A: Given,

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

Q: Use the definition of the derivative to solve.

A: To determine the derivative of the function.

Q: Find the second derivative of f(x) = 3e³* – 8e** -6.x 10)

A:

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: Find the second derivative of the function. f(x) = 7x3/2 f "(x) =

A:

Q: 4. Given the function y = 2x³ - 4x² + 5, find its derivative.

A: Differentiate with respect to x