For the function f(x) = find f'"(x). Then find f''(0) and f'"(4). %3D 2+x f"(x) =] Select the correct choice below and fill in any answer boxes in your choice. O A. f"(0) = (Simplify your answer. Type an exact answer.) %3D O B. f'(0) is undefined. Select the correct choice below and fill in any answer boxes in your choice. O A. f'(4) = (Simplify your answer. Type an exact answer.) O B. f'(4) is undefined.

Q: Which of the following equation defines a function? O y = 4 – 2 O 3x2 + 1y? = 16 O 6x + ly? = -–1 O…

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Q: Using implicit differentiation, solve for the following. 1. 2х-у--3 a. dyldx= 2. y²+x²=9 a. dyldx=…

A: When functions are not defined explicitly in terms of the variable that we want to differentiate…

Q: Differentiate the following using implicit differentiation 3/a + V = 7

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Q: After a recent flood the water level of a river is 43 feet, measurements show that it is receding at…

A: Given, W = fd = -3d +43  We have to find the formula for inverse function

Q: What is the equation of the function? O A. y = ()* ов. y = 3 OC. y = 2(- 3. O D. y = 2(3) 2/3

A: General equation of exponential function :

Q: Differentiate the following functions: 6. y = csc-(2sinx)

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Q: Differentiate the function g(x) = 6x² + 11tanx.

A: The function is given by gx = 6x2+11tanx To evaluate: The expression of g'x

Q: Given that h"(w) = -34. State the function that best describes h'(w). O a. h'(w) = -34w O b. h'(x) =…

A: Use the concept of power rule of derivative and select the option form given.

Q: 0.0400= I.100-x]L•100-X] (2x3

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Q: The derivative of the function - is equal to e Select one: a. a(2º In 2 + 1) b. e" (2ª In 2) c. e"…

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Q: Use the given graph of the function f to find the following values for

A: Since you have asked a question with multiple subparts, we will solve the first three subparts for…

Q: The derivative of the function Is equal to Select one: a. e"(2" In 2 + 1) b. æ(2" In 2 + 1) c. e2²+=…

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Q: Differentiate the function g(x) = 2x² + 5tanx. Answer g'(x) =

A: Given : the differenctiate Equation : g(x)=2x2+5tan(x)

Q: The graph of a function f is given. Use the graph to find the value f1 (3). Q 6-

A: For inverse function value of x and y get interchanged   Given f-1(x)=f-1(3) x = 3 , y = ? as  value…

Q: The graph of the second derivative f"(x) of a function f is shown. State the x-coordinates of the…

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Q: Use implicit differentiation to solve the following questions.  x^2-2xy+5y^2=6

A: Given:- x2 - 2xy+5y2=6 To find:- Use implicit differentiation to find dy/dx

Q: Choose the correct equation(s) for the function shown in the graph. Select all that apply. y %24 1.…

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Q: y = tan x² - 2x

A: Given: y=tan2x2-2x To Find: To differentiate the given function.

Q: State the rule that has to be applied first in order to differentiation the function y = -5te2t. a.…

A: We have a function y = -5te2t . Now we need to find which rule needs to be applied first to…

Q: g(b)= g'(b)= Calculate g(b) and g'(b) where g(x) is the inverse of f(x) - 18, where b 248

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Q: x²y3 + 3y* = 5x - 4y?

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Q: Q3/ Determine whether the following functions are harmonic or not. 1. 3xy + 5xy - 2y 2. 3x²y + 2x -…

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Q: Differentiate the function L(x) = -6e"(cscx + 7cotx). Answer L'(x) =

A: Given Equation : L(x)=−6ex(csc(x)+7cot(x))   L'(x)= derivative of L(x)

Q: create 2 sample word problems of basic rules of differentiation  with solutions

A: First problem: At what rate is the area of square increasing when the side increases at a rate of 2…

Q: Is the function y=sec x always defined? Why or why not?

A: y=secx

Q: Locate the stationary point of the following functions and determine their character. y= 1/2x^4 -…

A: Please see the below picture for detailed solution.

Q: 5. State the domain and the range of the tangent function.

A: Consider the tangent function Give the domain and range.   Since tan x=sin xcos x therefore, tangent…

Q: Find the indicated higher derivative of the given function. y = 4x² + 9x³-5x + 6; find y". y" = ||

A: Find the double derivative of the function  y= 4x4+9x3-5x+6

Q: V Determine whether the following functions are harmonic or not. 1. 3xy+ 5xy2- 2y3 2. 3xy+ 2x-…

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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: