2. If the derivative of an accurately determined function is replaced with a finite difference, how the choice of step influences the error of the replacement? Which of the three types of finite difference is the most accurate?

Q: Use the definition of the derivative to find the slope of the tangent line to the graph of the…

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Q: Sketch the graphs of two functions that have the given derivative: f'(x)=2

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Q: Find the derivative of the function.

A: Use the chain and quotient rule of derivative to differentiate the function.

Q: Suppose that you can calculate the derivative of a function using the formula f′(x)=3f(x)+1x. If the…

A: Derivative of a function using the formula f′(x)=3f(x)+1x and f(3)=6. We know that approximate…

Q: Show both the Newton and Leibniz notation for finding the derivative of y = f(x) = 4x5.

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Q: In(x²) What is the derivative of

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Q: - Use the definition of derivative to find the tangent and normal equations of f(x) = (x - 3)2 %3D…

A: We can find the tangent equation and normal equation as below.

Q: Find the derivative of f (x) = x at x = -4 algebraically. f' (-4) =

A: f(x)=x3 Find f'(-4)

Q: Suppose that the SECOND DERIVATIVE of a function f is given by f" (x) = (x – 2)² (x² – 4x). Find the…

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Q: Sometimes the second derivative test is harder to use, even if it applies. Use the first derivative…

A: Given,

Q: find the derivative of f (x) at the designated value of x. f (x) = x3 at x = 12

A: The derivative of a function can be calculated by differentiating both sides of the function with…

Q: Suppose that the second derivative of the function y=f(x) is y'' = (x-3)(x+9). For what x-values…

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Q: Suppose that the function y in the Derivative Product Rule has a constant value c. What does the…

A: Derivative product rule:The derivative product rule for the functions x and y is given by,

Q: What is the derivative of the following function?

A:

Q: Determine the derivative of the given function by using two different methods 2- 3) y = ² + 3

A: Given: y=x2-3x2+34

Q: Find the derivative of the function. (x) - In(4 - x") f'(x) -

A: Find the derivative of the function.      fx=ln4-x8

Q: Find the derivative of the following function by definition (from first principle): f(x)= x/(x-1)

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Q: Find a function whose square plus the square of its derivative is 1.

A: To Find a function whose square plus the square of its derivative is 1.

Q: Suppose the derivative of the function y = ƒ(x) is y′ = (x - 1) 2(x - 2)(x - 4). At what points, if…

A: It is given that, the function f(x) has the derivative

Q: Suppose 8 (x) =sec='(x<). what is the derivative of g with respect to x?

A: We can find the answer as below.

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: Where does the derivative of g(x)=(x^2)/((x^2)+3) = 0 or is undefined?

A: Given function, gx=x2x2+3

Q: Estimate the derivative of the function f (x) = - – 3 at the point x = 3. 3 3 1/5 1/3

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Q: Discuss the solution on how to get the derivative of the function

A: This question is related to differentiation, We will solve it using given information.

Q: Determine the value of X on which the derivative of the function Y = | 3x² + 4x + 1] does not exist.

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Q: If a function is decreasing with an upward concavity, what do you know about the function's first…

A: Given :   If a function is decreasing with an upward concavity To find : the function's first two…

Q: 5) Explain why the definition of a numerical derivative does not exist at x = 2 in the graph shown.…

A: The objective is to explain the reason definition of numerical derivative doesn't exist at x=2 in…

Q: What rule should be used in getting the derivative of y=(1−x^2 )^6

A: What rule should be used in getting the derivative of y=(1−x^2 )^6

Q: Use a quick approximation to estimate the derivative of the given function at the indicated point.…

A: Considering f(x) = 9 – 5x. To find the approximate derivative of f(x) at x = 2.

Q: Determine the derivative of the given function by using two different methods

A: Given,         y=x2-3x2+34

Q: What is the second derivative of f(x)=−x4? at the point x=−3 Do not include "f′′(x)=" in your…

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Q: Prove that the derivative of an even function is an odd function and then of an odd function is an…

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Q: 1) Use the definition of the derivative to calculate the derivative off(x) = 3x2-5x+ 1

A: Find the derivative of f (x) = 3x2 –5x +1.

Q: Use a quick approximation to estimate the derivative of the given function at the indicated point.…

A: f (x) = 1 − 2x  point,  x = 2 To use quick approximation to estimate the derivative, f'(2).

Q: Determine the value of X on which the derivative of the function y 3x2 + 4x + 1| does not exist.

A: Giveny=|3x2+4x+1|y=|3x2+3x+x+1|y=|3x(x+1)+x+1|y=|(3x+1)(x+1)|Using modulus propertyy=|3x+1||x+1|

Q: If fox) is odd function , then the derivative of y =coshf(-x)) equals

A: here option B is true

Q: Calculate the derivative of f1 (x) = √1−2x by using the definition of the derivative as the limit of…

A:

Q: 4. f(x)=

A: The given function is: fx=5x2x+3   As we know that; The Power Law: ddxxn=nxn-1 The Quotient rule:…

Q: ). Prove that the derivative of an even function is odd and that the derivative of an odd function…

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Q: 5. f(x) = [(x + 5)5 – 1]4

A:

Q: Suppose the derivative of the function y=f(x) is y’=(x—1)^2(x—2). At what points, if any, does the…

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Q: Which of the following is not an equivalent way of expressing the term "derivative?"

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Q: 2) Find the derivative of the function f(x) = 3x² by definition

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Q: Suppose we are asked to compute the 100th derivative of x 3 . How can we obtain the answer in a fast…

A: Solve the following

Q: 1. Use the definition of the derivative to find the derivative of f(x)- V-x-2

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Q: Suppose that the second derivative of the function y = ƒ(x) is y'' = x2(x - 2)3(x + 3). For what…

A: Given that, y=f(x) Second Derivative is y'' = x2(x - 2)3(x + 3). As we know that, Inflection point…

Q: In x g(x) = 2

A: