Part 1: A derivative computation using the chain rule Suppose F(z) is a differentiable function for all real numbers z. Evaluate the following derivative. Enter the derivative of F(1) using prime notation, i.e., as Part 2: The derivative of a definite integral

Q: 2z, z 1 f(z) =

A: Given fx=2x,   x≤12x,    x>1 Sketching the graph of function

Q: the Fundamental Theorem of Calculus to find the derivative of the function. Simplify answer 5x g(x)…

A: Topic:- calculus

Q: What is the derivative of a function ƒ? How is its domain related to the domain of ƒ? Give examples.

A: Define the derivative of the function f.

Q: Find the derivative of f(x): z²+2 . Enclose numerators and denominators in parentheses. For example,…

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Q: Part I: Find the derivative. Show all workow all 7. f(x) = e?*(x' – 2x+1) %3D

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Q: Part 1: The derivative at a specific point Use the definition of the derviative to compute the…

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Q: Part 1: Use the definition of the derviative to compute the derivative of f(x)=1−8x2f(x)=1−8x2 at…

A: Given: f(x)=1-8x2 Formula used:

Q: utolial Exeicise Use the Quotient Rule to find the derivative of the function. cos(t) (t) = %3! Step…

A: Use quotient rule for finding the derivative .

Q: -가 Question-2 a) Find the derivative of f(x) = 2x? –- at x = 3 using definition of derivative at a…

A: As per our guideline we are supposed to be answer only one question

Q: f(x) = |V Use part I of the Fundamental Theorem of Calculus to find the derivative of f(æ) = |.…

A: Using part 1 of fundamental theorem of calculus.

Q: a (x - 9)2 Let f(x) = (x2 + 7)° Use logarithmic differentiation to determine the derivative. f'(x) =…

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Q: Let g be a function that is defined for all x, x # 2, such that g(3) = 4 and the derivative of g is…

A: Here, g(3)=4 & g'(x)=x2-16x-2, x≠2

Q: 2. What is implicit differentiation? When do we use it? Give examples.

A: What is implicit differentiation and when do we use and give examples

Q: Question 8 X-2 If f(x) = x2 +4 then what is the derivative of f at x=-1?

A: Given! f(x) = (x-2)/(x2+4).

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A: We find V(x) in step 2

Q: Graph of f(x) is provided in the image. Sketch the graph of the derivative function f'(x).

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Q: Part C: Graphical interpretation of the derivative. 7. Which of the following graphs below is f(x),…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: finding the local mins and maximums and the intervals of increase and decrease and making a sign…

A: Consider the graph of the function:

Q: Use the definition of the derivative to compute the derivative of the function f(x) = vx + 8 at an…

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Q: Question 1 definition of the derivative (do not use general derivative rules). Be sure to specify…

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Q: definition for the function above to find the derivative. f'(x) = lim Ax →0 (x + Ax)? x2) Ax 12 – x2…

A: Using the definition of derivative,

Q: these are review questions for exam, i was absent when these were covered please help with #9 and…

A: Since you have submitted two questions, we'll answer the first question. For the second question…

Q: () Use part I of the Fundamental Theorem of Calculus to find the derivative of 17 F(x) tan F'(z)=…

A: Topic-  derivatives of definite integration

Q: 21-31 Find the derivative of the function using the definition of derivative. State the domain of…

A: The domain of the function f is, dom(f) = R, which is the set of all real numbers. And, the domain…

Q: 7 1 lim represents the derivative of some function f(x) at some number a. Find f(æ) and a. f(z) = a…

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Q: Question 1 definition of the derivative (do not use general derivative rules). Be sure to specify…

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Q: Find the derivative of f (x) V8x+1 Enclose numerators and denominators in parentheses. For example,…

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Q: Question Determine the derivative of f(x) = In(xV? + 1). Provide your answer below: (x) =O

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Q: 2. Which statement is not true? a. If a function f (x) has a derivative at x, then it is said to be…

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Q: - Part 1: A derivative computation using the chain rule Suppose F(x) is any function that is…

A: Given that : ddxFx4=x4+4x3 . We can re-write it as : dFx4=x4+4x3.dx Therefore, we can achieve F(x)…

Q: 3 If f(2) - 8, and f'(2) 4 - 1 Let f'(x) be the inverse function of f(x). (f-1)'( - 8) = - 1 Write…

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Q: Part 1: The derivative at a specific point Use the definition of the derviative to compute the…

A: To find the derivative of f(x)=1-7x2 at the point x=3 using the limit definition.

Q: Example: Let f(x)=x^2-1/x^2+1 The first derivative is shown in the image below.

A: Given f(x)=x2-1x2+1

Q: Question 1 definition of the derivative (do not use general derivative rules). Be sure to specify…

A: Since you have asked multiple questions in a single request we would be answering only the first…

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A: The function f(x)=x2. We have to answer the following... Solution (a). f(x)=x2⇒f'(x)=2x Estimated…

Q: Suppose F(x) is any function that is differentiable for all real numbers x. Evaluate the following…

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Q: a) Sketch the graph of the function f (x) = {2x – 3 if æ 2 then evaluate lim f(x), lim f(x) at a =…

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Q: 1800 function Find the derivative of the following x3 F(x) = = 1²12²₁ = X5 (2t - 1)³ dt using the…

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Q: Page > of 2 1. Find the derivative of function z. Assume A and B are constants. + Bey

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Part 1: A derivative computation using the chain rule Suppose F(x) is a differentiable function for…

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Q: a) Use the limit definition to find the derivative function, h'(x), of the given function h(x). 2…

A: The derivative of f(x) with respect to x is given as limh→0f(x+h)-f(x)h

Q: Sketch the Gaussian function (like as a picture below). In the same graph, draw its first derivative…

A: A Gaussian curve is of the form fx=ae-x-b22c2 ,c>0a, b, c are constants with a bell-shaped…

Q: Use Part 1 of the Fundamental Theorem of Calculus to find the derivative of the function. •tan(x) 3t…

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Q: Find the derivative. (The Fundamental Theorem of Calculus -- Part 1) 19) y = cos ft dt COS-

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Q: Example 3.25 f (1,2) = 3 and the derivative of the function f at the point (1,2) in the i + j…

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Q: (a) Use Definition 5.2.1(Differentiability). to produce the proper formula for the derivative of…

A: The definition for the differentiability of a function fx at point c is given by f'c=limx→cfx-fcx-c.…

Q: Part I: Find the derivative. Show all workow all y = e$x²-x 3.

A: The given equation is: y=e5x2-x

Q: 5. a) Identify f, f', and f' from the graph below. b) Sketch the graph of the derivative in 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: