Given f(x)=In(x2 -1)-3 where x<-1, find its inverse function f -1(x).

Q: For the function f(x) = 4x- 3x +2x +6x +2, find f"(x), the third derivative of f, and f''"(x) = %3D

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Q: Find the derivative of the function. g(x) = √(4 − 3x2 )

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Q: Given g(x) = ln(5x³ + x), the derivative g' (x) is

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Q: 1. Find the derivative of f(x). 3x³ 2x²-x-5 - (a) f(x) = √x (b) f(x) =

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Q: 1. Find the derivative of f(x) if f(x) = x7 + 10x5 – x² – 4

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Q: Given f(x) = x² + 1, x 2 0, Find the derivative of the inverse at the point (5, 2) (do not find f-1)

A: Let's find.

Q: Find the derivative of the algebraic function. f(x) = (x2 + 5x + 6)/(x2 − 4)

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Q: Find the second derivative of the function f(x) = 5x2(x + 47) %3D

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Q: Find the derivative of the function g(x)=(3x^2−4x+3)e^x g'(x)=

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Q: Find the first, second, and third derivatives of f(x) = x^4 − 2x^3 + 2x^2 − x + 8.

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

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

Q: Give the derivative formula for the function g(x) 2.1X 2 g '(x)

A: The given function is

Q: Find the derivative of h(x) = x 2(9x + 2).

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Q: x=1), 3. Y = In (x-1), (х-2)2

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Q: . Y= In (- (x-2)2

A: To solve the second derivative of the function

Q: Find the derivative of the function. g(x) = (1 + 5x)5(4 + x – x²)7 - g'(x)

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Q: Find the third derivative of the function f(x) = (1) / (2x-1)

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Q: From a function f(x) = 5000 x2 - 7000x + 12000   Find the first and second derivatives

A: dxndx = nxn-1 dcfxdx = c df(x)dx ; where 'c' is constant.

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

A: f(x)=x3-6x2+12x

Q: Find the second derivative for the function f (x) = 4e . 1 - 2x3

A: Given: fx=4ex-12x3 for finding second derivative of given, we find first derivative then find…

Q: 17. f(x) x²(2x+3) (x² +1)*

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Q: Find the derivative of f (x) = e(x3 − 10x2 + 8 ) .

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Find the second derivative of the function. In(x) f(x) 6x2 f"(x) =

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Q: Find the second derivative of the function. g(x) = 9/x + e6× In(x) g"(x) = %3D

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Q: Find the derivative of the composite natural exponential functions 1. f(x) = In x² x-2 2. g(x) =…

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Q: Let f(x) = 4 −(1/3)x3 . Determine the derivative (f -1)'(x) of the inverse function to f.

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Q: Given f(x) = 5x² + 5x + 2, find f' (x) using the definition of a derivative.

A: Given function is solved through derivative  detailed solution is given below

Q: y = In (*+1) °(x+1), (x+2)3

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Q: Find the second derivative of the function.       f(x) = x2 + 3x−3

A: Given: fx=x2+3x-3

Q: e2x -e-2x e2x+e-2x

A: Solving the problem by finding the second derivative.

Q: Let f(x) = 4 – x³. Determine the derivative (f-1)'(x) of the inverse function to f.

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Q: Find the derivative of the inverse function  f(x) = x/x+2

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Q: Find the second derivative of h(x)=x2+3x-3 Simplify your answer, if possible.

A: Our objective is to find the second derivative of h(x)=x2+3x-3.

Q: Find the second derivative of the function. In(x) f(x) = + 6x? -4x° – 18xln(x) + 3-6 ln(x) + 12…

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Q: Find the derivative of the function f ( x ) = x2−10x+3 using First Principles.

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Q: Find the derivative of the function. g(x) = In(x – 5.1x=1) g'(x) =

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Q: Find the second derivative of the function. f(x) = (3x° + 6)*

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Q: Find the derivative: g(x) = 6x² e- X O g'(x) = 6xe (2-x) Og'(x) = -12xe** O g'(x) = 6xe (2-x) O…

A: We have to find derivative of given function.

Q: the derivative of the function g(x) In(lx2 +21)

A: We have to find the derivative of g(x)=ln(|x2+2|)

Q: Find the second derivative of the function f(x) = 8/(x − 2)2

A: Find the second derivative of the function f(x) = 8/(x − 2)2

Q: Find the third derivative f"" for the function f(x) = I-5

A: The first derivative of is given as: Also the derivative of a function in form of is: The given…

Q: Let f(x)=4-1/3x^3. Determine the derivative (f^-1)'(x) of the inverse function to f.

A: Derivative of inverse function is

Q: #12) Find the derivative of the function f(x) = 35x2-1

A: The solution of the problem is given in the next step.

Q: find the derivative  f(x)=x2(x3-1)

A: Apply the product rule and obtain the derivative of the given function.

Q: Determine the 3rd derivative of the given function f(x) = (3x² - 5x + 6)4.

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Q: Find the second derivative of the function. f(x) = 8(2 − 2x)4 f"(x)=

A: Given,

Q: Find the derivative of the inverse of the given function at the specified point on the graph of the…

A: To sketch the graph of the function f(x) and determine the value of the derivative of inverse of the…

Q: Find the derivative of f(x) = e2" (3x² – x) %3D

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Q: Given g(x) = ln(7x5 + x), the derivative g' (x) is 7x5 + x 7x5 + x 35x4 +1 O 5x4 O 35x4 + 1 35x4 + 1…

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Q: 3 f(x) = (x³ – 8)4 f'(x) :

A: Use Chain Rule with other some basic identities.