5. Find the inverse functions of these real functions. (a) f(x)= x/5+5 (b) f(x) = 3r* + 2

Q: Suppose that the differentiable function y = f(x) has an inverse, that the graph of f passes through…

A: first we find equation of line which passes through (2,5) and slope (m)=1/4 y-5=m(x-2)…

Q: What is the first derivative of the following function: f(x) = (x³ + 2)4 O f'(x) = 12x²(x³ + 2)³ O…

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Q: Find the first derivative f' and the original function f. f"(x) = x³ – 4x + 6, f'(0) = 9, f(0) = 6…

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Q: Q-2) Prove that converting the Higher-Order derivatives to the finite difference formula would be:…

A: Hi! Thank you for the question, As per the honor code, we are allowed to answer one question at a…

Q: The derivative to determine whether the function is strictly monotonic on its entire domain and…

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Q: Find an equation of the tangent line to the graph of the function at the given point. f(x) = (1 −…

A: The equation of the function  f(x) = (1 − x)(x2 − 3)2

Q: 4x - 4 if x > 2 Suppose f(x) = Find f'(2) using the definition of derivatives. if x < 2

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Q: The derivative to determine whether the function is strictly monotonic on its entire domain and…

A: We have given fx=1-x3-6x5 By differentiating the function, f'x=-3x2-30x4=-3x21-10x2 Now, we find the…

Q: 1. Determine if the function is even or odd x*+1 g(x) = f(x) = sin x x3-2x

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Q: 2. Find the derivative of (a) f(x) = x4 +2x-2 + 4ex

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Q: Consider the function, f(x) = (x + 1)ln(5x² + e). Without finding explicitly the inverse of f(x),…

A: Given : fx = x+1ln5x2+e

Q: (3) Let y = f(x) = x2 +1, evaluate the derivative of the inverse function x = f-(y) at y = 2. %3D

A: Given :           y=fx=x2+1

Q: If f(x) = 2+ |x − 3| for all x, then the value of the derivative f’(x) at x = 3 is

A: Given;. f(x)=2+|x-3| f'(x)= ?

Q: 4. Suppose that f(4)= 2, g(4)=5, f'(4)=6, and g'(4)=-3. Find derivative h'(4) in (a) - (d). (a)…

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Q: -what is the second derivative of i (-1) when i(x) =x^2f(x) -What is the derivative of g(3) when…

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Q: In(3æ) Given f(x) the derivative f'(x) is 3 3 1 3x 1 3 1 3x

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Q: Find the derivatives (1st of the ff. function or as specified in the problem. Simplify the…

A: given: f=x3y2-yx+lnx to find:fyyxxx

Q: 1) Find the hundredth derivative of p (x) = (x + x° + x')'º(1 + x²)'' (x³ + x° + x'). Justify your…

A: Here we have to find the hundredth derivative of p(x)=(x+x5+x7)10(1+x2)11(x3+x5+x7) .

Q: if f(x) = x² √In x² x . find the derivative of this function f'(x A. f'(x) = B. f'(x) = c. f'(x) =…

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Q: if f(x) = x²√In x² x . find the derivative of this function f'(x) A. f'(x) = B. f'(x) = c. f'(x) =…

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Q: 1 Find the derivative of the following function: f(x) = e2X(3x² - vx) 2e2X(6x - 1/x) O e'(6x -…

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Q: МАТ 115 1.Find the derivative a. f(x) =x' In x b. f(x) = (x'+x-1) %3D с. f(x) d. f(x) = 4e*- x 3D20…

A: As per barlteby guideline for more than one sub question asked only first three are to be answered…

Q: 1. Find the first derivative of the function g(x) = 6x+ 27r'+36x. g'(x) 18x + 54r +36 2. Find the…

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Q: 7. Find and sketch the domain of the function f(x, y) = 2 ln(49 – x² – y²) + 8/ -

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Q: if f(x) = x²√√In x² x . find the derivative of this function f'(x) A. f'(x) = B. f'(x) = c. f'(x) =…

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Q: -3- 6. USE THE ALTERNATIVE FORM OF THE DERIVATIVE TO FIND THE DERIVATIVE (IF IT EXISTS) OF f(x) = x²…

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Q: 十2, What is the inverse function of y = ? T-2 Oy= 2(+1) 7-1 %3D 2z-2 O y = -1 2(+1) O y= -1 2-1

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Q: 7–46 Find the derivative of the function. 8. F(x) = (1 + x + x²)9

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Q: Find the domain of the function. g(x) = ln(x - 1)

A: A function is a relation between an input variable and an output variable wherein each input…

Q: 3. Find the derivative of the following function using the formula. f(x + h) – f(x) lim h a. f(x) =…

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Q: 1. Consider the function f ( x ) = 1 + 1/10 x3 + 1/25 x5 .  Select any point ( a , f -1 ( a ) ) on…

A: Given function : f(x)=1+110x3+125x5 To solve the given problem first we need to find the inverse of…

Q: if f(x) = x²√√In x² A. f'(x) = B. f'(x) = c. f'(x) = D. f'(x) = find the derivative of this function…

A: Given,            fx=x2lnx2xTo find : Find the derivative of the given function.

Q: 1) Use the Product Rule or the Quotient Rule to find the derivative of the given function a – g(x) =…

A: The objective is to use the product rule or quotient rule to find the derivative of the given…

Q: In(5æ) Given f(x) the derivative 5 f'(x) is 1 5x 5 1 5x 1

A: given f(x)=ln(5x)5 Note- 2 different questions (Multiple)are asked, I am answering first.

Q: f(x) = x2 -1

A:

Q: Question 2: Use this property of polynomials to calculate the derivative of 3 + x³, by first…

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Q: - Show that f(x)= E ƒ(x), where E is a constant and f(x)= e²x + e2x

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Q: 5.) f (x) = 2x² – 3x – 5 Зх —

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Q: 1. Compute the first, second, and third derivative of a. f(x) = x² In(x+1) b. h(x) = x² sin x

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Q: 1 If f(6) = 3, and f'(6) 2 Let f'(x) be the inverse function of f(x). (f ')'(3) = Write the equation…

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Q: 8) Find (f-1)'(a) for each (the derivative of the inverse of function f). f(x) = x³ + 2x + 3, a = 0…

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Q: Find the first and second derivatives of the function. f(x) = (3x2 + 8)7/2 f '(x)  =        f ''(x)…

A: The given function is fx=3x2+872.

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

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Q: 1/3 Find the absolute extrema of the function f(x) = (x + 16) on the interval [-5,2]. Find the…

A: To find: Absolute extremum of the given function.

Q: 7) Show that the function ƒ(z) = z² +4 has no inverse function.

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Q: A function, f (x), has derivatives: f'(x) = x² (x – 3) f"(x) = 3x(x – 2) Which of the following…

A: Consider the derivatives of the function fx f'x=x2x-3f''x=3xx-2 First, find the original function…

Q: Find the domain of this function. f(x) = ln(x - 8)

A: We have to find domain

Q: 5. Find a function f(x) whose derivative is f'(x) = +1. (Hint: (x + 1)/x=1+1/x)

A: 5) derivative of a function is given, to find the function we have to find the anti derivative of…

Q: 8. Find f '(2) if f(x) = [g(x)]*, and g(x) = x + 2

A: g(x) = x+2  f(x) = [g(x)]4  f(x) = (x+2)4