Composite Functions: What does (f*g^(-1))(x) and (g^(-1)*f)(x) stand mean, how do you solve them?

Q: Differentiate the function. f(x) = 5x ln(3x) − 5x

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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: As you will show, exponential growth functions ekx always dominate power functions x", and power…

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

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Q: Evaluate the second derivative of the given function for the given value of x. 2 3 4 y 3x --,X%= -8…

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Q: Verify f(x). direction delta function 8(x - a)

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Q: limit.

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Q: 2- 3x- 3X- %3D

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Q: • Why do we need the Chain Rule in implicit differentiation? Show with an example and describe how…

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Q: Differentiate the function. f(x) = ln  7   x f '(x) =

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Q: Calculate root and error %. Find the root of the equation fx=ln(x)-5+x in the interval [2.5, 3.0]…

A: Consider the given information.

Q: Derivative at Different Points Without doing ANY additional computations, complete the table of…

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Q: Find first and second derivative, critical points, concavity, x and y intercepts, vert and horz…

A: This question contains multiple sub-parts and you have not asked any specific sub-part. As per the…

Q: Differentiate the function using any appropriate method

A: Here g(x) is in the form pxqx so here we use division rule of differenciation to find the derivative…

Q: y = 1.2889x3 - 358.53x2 + 48536x - 34188 What is the second derivative, what is the point of…

A: we have been given an equation  y=1.2889x3-358.53x2+48536x-34188 to find the inflection point we…

Q: Discuss the relationship between the secant line, slope of the tangent line, derivative of a…

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Q: An isosceles triangle is inscribed in a circle of radius 4 cm. find the base and the height of the…

A: let height of triangle is H  and given radius of circle is R=4xm

Q: The tangent line at x = 5 to the graph of f(x) = x passes through the points (5, f(5)) and (6, 200).…

A: Given, f(x)=x³ Therefore, f(5)= 5³= 125

Q: Why did you take f'(x)=0 and from them I didn't understand, can you explain it a bit, its really…

A: We have to explain the term f'(x)=0.

Q: Discuss the role of the central difference method to approximate the numerical derivative of a given…

A: Note:-  If you get a question that has more than 1 question, please answer the first question,…

Q: Sketch graph also determine the location of critical point and determine its nature? (Second…

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Q: Locate any relative extrema and points of inflection. Use a graphing utility to confirm your results…

A: Given: y=2x- ln 2x

Q: (omputale the derivative 8. Y= (9+

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Q: In finding the derivative of a root (a cube root in this case), where are all of these numbers…

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Q: eliminate the constant using any methods (by isolation of constants or by differentiation and…

A: Given: xsiny - ycosx = c We are using the method of differentiation to eliminate the arbitrary…

Q: function given by

A: Given, X and Y have a joint probability density function                    fX, Y(x, y)=ce-3x-5yif…

Q: Zez analytical function or not?

A: We check whether w=zez is analytic function or not.

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

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Q: The derivative of a function g (X) is g'(x) = x“ +2x - 8 = (x – 2) (x + 4). Find critical point(s)…

A: g'(x)=(x-2)(x+4)

Q: ifferentiate  y=sin2(sin3x)-(sin(x3+2)/x)

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Q: d 14.- - (logx) dx

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Q: 4-X

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Q: What does it mean when a function does not have any critical numbers. Please explain ALL…

A: Critical numbers for any function are defined as the real number x in the domain of the function…

Q: Draw simple graphs of the first and second derivatives of the function y = f(x) whose graph is given…

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Q: Find all local maximum and minimum for f(x) = 2x +3x² – 12x using the first derivative test. Show me…

A: Given - fx=2x3+3x2-12x To do - Find the local maximum and minimum using 1st derivative test.

Q: 5 - x2 + 2x – 3 = 0

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Q: using logarithmic differentiation, find the derivative of y=x(2-x)

A: TO FIND THE DERIVATIVE OF   Y=X(2-X) 1. TAKE 'LOG' ON BOTH SIDES. 2.DIFFERENTIATE WIYH RESPECT TO…

Q: Graph of ln x

A: Given,         The function is fx=lnx.

Q: Find all critical values, local extrema and the absolute maximum and absolute minimum values of…

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Q: Point estimation of H-Hzis X-X2 صواب ihi

A: Use the theory of confidence interval of point estimation.

Q: e second derivative test, If f(x) - 4x + 2 then f(x) has a local maximum at the point x = 3 -2

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Q: Differentiate the function. h(x) = ex9 + ln(x)

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Q: QI. Find the derivative of f(x)= 2x² - - by using the definition of derivative.

A: We have to find derivative

Q: 3. Give an example of a situation in which composite differentiation might be used. Give examples of…

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Q: find and evaluate the derivative of the function at the given point. Use a graphing utility to…

A: Given,            ft=3t+2t-1 , 0,-2

Q: Two positive numbers have a product of 81. Find the minimum possible value of their sum.(You must…

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Q: Differentiate the function. f(x) =  5   ln x f '(x) =

A: Given that: f(x)=5.lnx

Q: what is the basic concept of a derivative? How is this derivative calculated? What techniques/rules…

A: Use the definition of derivative

Q: Using two phase method if min f-0.go to phase II

A: this is true because if we use two phase method than minf=0 convert in maxf=0

Q: orrelation function:

A: Given as, Rx 0=3, Rx ±1=2, Rx ±2=1, Rx l=0, l>2