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

Q: Explain how the first derivative of a function determines where the function is increasing and…

A:

Q: What is an instance where a function doesn’t have the same domain as its derivative? Give an example…

A: The domain of a function f(x) is the set of all the x-values for which the given function is…

Q: Find a rule for the derivative of the product of four functions f,g,h, and k. Use your result from…

A:

Q: 2h lim h→0 h(/2x+2h+/2x)

A: Given, limh→0 2hh2x+2h+2x The definition of derivative is given by fx=limh→0 fx+h-fxh

Q: Explain the relationship between a function and the derivative by providing an example.

A:

Q: Describe the two methods that help to differentiate the equations implicitly, and find the…

A: The two methods that help to differentiate the equation implicitly and derivative…

Q: Below is the graph of a function. Which of the following could be a graph of its c 3 2 1 -2 T3/ 1 2…

A:

Q: 2. The graph of f is shown in the figure. Sketch a graph of the derivative of f. 4 6 " •

A: We have given a graph of f(x):

Q: y = 2 7x²)*(1 + 9x)² (sec²(x^))(tan³(x¹)) (x³ - 7x²3) 4 (1

A:

Q: Which functions have a negative first derivative for all x?

A: Which functions have a negative first derivative for all x?

Q: Which defines as the process of finding the derivative of a function? *

A: Here, to tell which defines as the process of finding the derivative of a function.

Q: How do I find the derivative of this? Isn't it the Quotient rule?

A: Given,

Q: why setting the derivative of a function equal to zero allows us to find the maximum or minimum…

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Q: what is an example of a composite "function-in-a-function" and find its derivative using the chain…

A: We have to give an example of composite function, and find the derivative using the chain rule

Q: (a) Use the figure below to rank the quantities A = f'(1), B = f' (2), C =f'(3) from smallest to…

A: Derivatives by graph

Q: LY 5- -4 2- -5 -4 -3 -2 -14 -2+ -3

A:

Q: The Power Chain Rule simplifies computing the derivative of a powerof an expression

A: To find the derivative of a power of an expression using the chain rule. ddxe3x+1 Solution: Chain…

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

A: In this question, we have the graph for the function f(x). Here, we need to find the graph of its…

Q: how to get derivative of 2(x+(16/x))

A: The objective of the question is to find the derivative of the function 2(x+(16/x)). The derivative…

Q: What is the rule for calculating the derivative of a composition of two differentiable functions?…

A: Let f(x) and g(x) be two differentiable functions and their composition is

Q: Example 4:- By using the four steps rule, find the derivative of the function f(x) = Vx + 2

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Q: y" +6y' +10y=0; y(0) = 2, y'(0) =

A:

Q: determine a function by being given the function’s first derivative and an initial condition for the…

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Q: Given the graph of the function y = g(x) on the interval [0, 7]. The graph of g has an inflection…

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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: