Let f (x) = Using the centered 3-point formula for 1st derivatives: (x+1)= f'(0) -0.502509 using h = 0.1 f'(0) x -0.500626 using h = 0.05 Applying Richardson's extrapolation on the above values, we get a better approximation of f'(0) which is: -0.499998 O 0.234256 0.249999 -1.99985

Q: Let h(x) = f(g(x)) and p(x) = g(f(x)). Use the table below to comput derivatives. a. h'(2) b. p'(1)…

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Q: Find the derivative of the following function by first expanding the expression. f(x) = (6x + 1)…

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Q: Find the derivative of the following. Explain which rules of taking derivatives have been used and…

A: We will use chain rule twice for this problem

Q: use the table of values to calculate the derivative of the function at the given point. f(2x +…

A: To differntiate f(2x+g(x)), with respect to x, use the chain rule of differentiation,…

Q: Find the derivative of f(x) = 3x° cos(x). 8 CoS f'(x)

A: Given query is to find the derivative of the function.

Q: Find the derivative. f(x) = 8/ 4x + 7 f'(x) = |

A: Find derivative use Chan rule  And use d/dx(x½)=1/2(x)½

Q: Let f(x) = Using the centered 3-point formula for 1t derivatives: %3D (x-2) f'(0) 0.251255 using h =…

A: According to the Richardson's extrapolation formula, the true value of the derivative at any point x…

Q: Use the table to find the following derivatives

A: Given Data: x 1 2 3 4 5 f'(x) 3 5 2 1 4 g'(x) 2 4 3 1 5 From the above data,

Q: Let f (x) = (x+1)= Using the centered 3-point formula for 1st derivatives: f'(0) & –0.502509 using h…

A: Solution:

Q: Let f(x) = Using the centered 3-point formula for 1st derivatives: %3D (x-2): f'(0) & 0.251255 using…

A: Solution:

Q: Find the derivative of h(x) Provide your answer below: h'(x) = tan (3x + 1).

A: We have to find the derivative of the given trigonometric function.From the differentiation rule-

Q: Determine the derivative of the function f(x) = ln(1-x²) in the point zo = -0.5 using three-point…

A: The three-point central difference formula to calculate f'(x) can be defined as…

Q: find the derivative of f (x) at the designated value of x. f (x) = 1/x at x = 2/3

A: Given: f(x)=1x To find the derivative at x=23

Q: Find the derivative of the function at the given number. f(x) = x² - 9 at 0 f(0) =

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Q: Give the derivative formula for the function. h(x) = 12(1.7*) h'(x) =

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Q: Let f(x) = Using the centered 3-point formula for 1st derivatives: %3D (x+1)3 f'(0) -0.502509 using…

A: The Richardson's extrapolation for the centered 3 point formula is f'x0=Ah2+Ah2-Ah3. Here Ah,Ah2 are…

Q: Use the alternative form of the derivative to find the derivative at x = c (if it exists). (If the…

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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: