Find f(x) and g(x) so that the function given can be described as y = f(g(x)). y = esin x g(x) = [ ? ] 1= e*

Q: Find the critical point and the interval on which the given function is increasing or decreasing,…

A: Explained below

Q: find the absolute maximum and absolute minimum values of ƒ over the interval. ƒ(x) = (4/x) + ln x2,…

A: Given,

Q: Find the local and/or absolute maxima for the functions of the specified domain. Y= 1/(x-x^2) over…

A: Here we have to use the concept of derivatives. Here we use second derivatives test for finding…

Q: Find the local minima/maxima of -x + ln x if it exist

A: fx=-x+lnx Differentiating with respect to x, we get f'x=-1+1x Now to find critical values, solve the…

Q: Perform a first derivative test on the function f(x) = /x In 4x; (0,0o). a. Locate the critical…

A: Given functionfx  =x ln4x     ; 0,∞

Q: Find f"(x) for a) f(x)= lnx - ln(1/x)

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Q: .) What is the inner and the outer functions? b.) What is the derivative o

A: Given : The function is f(x) = x2+ 3x +1 .

Q: Find the first derivative of each function. a) f(x)=ln (e^x+e^-x)

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: The derivative of the function f(x) =x ln x is: a. f'(x) = In x +1 b. f'(x) = ln x +. c. f"(x)= In x…

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Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing. ƒ(x) = x2 ln…

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Q: Use the graph of the first derivative function f'(x) to find x values at which function has relative…

A: First of all, consider the graph of f '(x).

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

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Q: (b) Sketch the graph of f (x) = ln(4 – x²). Use the first and second derivatives to identify where…

A: Consider the function  fx=ln4−x2

Q: f(x)=ln(1+x/1-x) is function even or odd

A: We have to find the given function is either even or odd: fx=ln1+x1-x We know that for even function…

Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: fx=cosxxn When n=1, fx=cosxx Differentiating with respect to x, we get…

Q: Question1. Find the derivative w.r.t x. i. f(x) = Cos (3Vx) f(x) = x - x. Also draw the graph of…

A: given,        1.  fx=cos23x2.  fx=x3-x3.  fx=logxx2+1

Q: a) For the function f(x) =1-3x? , find f'(a) at a =-1 by using the definition of derivative. (a+b b)…

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Q: 10. Find the critical points of the following function. Use the Second Derivative test to determine…

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Q: Differentiate the following function Y=ln(x^2-1)/(3x+2)^2

A: Derivative of logarithm function

Q: find the extreme values on the interval f (x) = x − 12 ln x, [5, 40]

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Q: ■ Find y 2    implicit differentiation.   x3 + y3 = 1

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Q: Let h be a function that has second derivative (x+ 1) (x – 2) (x + 4)e5 h"(x) Is x=2 the…

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Q: For function, find (a) the critical numbers; (b) the open intervals where the function is…

A: Consider the function, y=x-4ln3x-9 Differentiate the given function with respect to “x” then,…

Q: Using logarithmic differentiation, Show that y(x)=xa2xex2 has no stationary points other than x=0,…

A: Given function is yx=xa2xex2. We have to show that the given function yx has no stationary points…

Q: A continuous function y = ƒ(x) is known to be negative at x = 0 and positive at x = 1. Why does the…

A: Given that f(0)<0 and f(1)>0  f(x) is a continuous function.

Q: Use y = (x2 - 6x)² and its derivative Y = 4x(x – 3)(x – 6) to find each of the following. dx Find…

A: This question is related to application of derivatives.

Q: he value x = ! is a critical number of the function f(x) = x ln(x), which has x) = 1+ ln(x). Use the…

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Q: Solve for the derivative of the given functions using the Chain Rule formula. a.) Let f(x) = √(x2 +…

A: Solution

Q: find the absolute maximum and absolute minimum values of ƒ over the interval ƒ(x) = x - 2 ln x,…

A: The given function and the interval is,

Q: 2 2x +1 Let f(x) =- |- log, (x² + + 1) • (b* - 5b +3)x +c. If f(x)isa tan decreasing function of x…

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Q: find the absolute maximum and minimumvalues of each function on the given interval. y = 10x(2 - ln…

A: Given function is:                              y=10x(2-ln x) over (0, 2e)   To determine:…

Q: 2. Given f(x) = x³ – 2x² + x + 2, find x e (-1, 3) such that f'(x) = 5. 3. Compute the derivative of…

A: Since you have posted multiple questions, as per our guidelines we are allowed to answer the first…

Q: The first derivative of the function h is given by h'(x) = tan(0.1x- x) for -n < x < R. On what…

A: Solution Given h'(x)=tan(0.1x3-x) for -π&lt;x&lt;π.we need to find on what intervals is h…

Q: Use y = (x² – 6x)² and its derivative = 4x(x – 3)(x – 6) to find each of the following. dx Find the…

A: we'll answer the first question since the exact one wasn't specified ,please submit a new question…

Q: Find the absolute maximum and minimum vaules of the funct ion g(x)= (x^2-3x+4)/(x-1) on the interval…

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Q: Solve for the derivative of the given functions using the Chain Rule formula.Let g(x) = sin (cos…

A: Since, g(x)=sin (cos x)g'(x)=cos (cos x)ddxcos (x)⇒g'(x)=cos (cos x)(-sin (x))ddx(x)⇒g'(x)=-cos (cos…

Q: The graphs of the derivatives of the functions F, G & H are shown below. Which of the functions have…

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Q: Find the derivatives of the function f for n = 1, 2, 3, and 4. Use the results to write a general…

A: Given:fx=cos xxn for n=1,2,3,4Formula:ddxuv=vu'-uv'v2

Q: 4. The graph of the first derivative f'(x) of a functionf is shown below. At what values of x does f…

A: Given graph of f'(x) is The value of x where f'(x)=0 are called as critical values where extrema…

Q: If Z = In(x² +y²), find-

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Q: 2) Use the chain rule. (Chapter 2.5) Find the derivative y= (x² +3x)*

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Q: The function f(x) = (8x – 1)e® has one critical number. Find it. 4x - x =

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Q: It works using the second derivative [ osxs] 1. Find the maximum and minimum limits of the function…

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Q: g(x)= cos2x/x2

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: On the graph of f(x)=cosx and the interval [−2π,0), for what value of x does f(x) achieve a minimum?

A: We know,  -1≤cos x≤1 for any real value of x.

Q: The function f is continuous for all real numbers and the graph of its derivative function f' is…

A: Given The graph of the derivative of a continuous  f

Q: 4 For the function f(x) = 6x + =, find the critical numbers and use the First Derivative Test to…

A: To find the critical number and maximum and minimum.

Q: The derivative of the function f is given by ƒ'(x): = e¯* cos(x²), for all real numbers x. What is…

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Q: Can you help step by step please?

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Q: Given f(x)=x(x-1). a) Find first derivatives of function f(x) using product rule and chain rule.

A: Our objective is to find the derivative and critical points.