f(x) = 5* – 4 is a 1-1 function. Determine its inverse function f¯'(x).

Q: Find the first and second derivatives of the function. f(x) = In(x + 4) f'(x) = f"(x) I3D

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Q: Find the derivative of f(x) = (3x – 2x?)’using the chain rule %3D

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Q: Find the derivative of the function.

A: Given: To find: Derivative

Q: Compute the derivative f'(x) for f(x) = log(x*) sin(x³).

A: Topic - derivative

Q: Find the derivative of the function.

A: Given function is By using the properties of logarithm, ln(a/b)=ln(a)-ln(b) and ln(a^b)=bln(a), we…

Q: Find y" by implicit differentiation. x² + 4y² = 4

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Q: Find the derivative of f(x) = In(x² + 1) %3D

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Q: Find the derivative of 2 cos x 1. f(x) x+1

A: As we know that: The Power rule: ddxxn=nxn-1 The Quotient rule: fg'=f'·g-g'·fg2 Given: fx=2cosxx+1

Q: Find the derivative of k(x) = log3(x) cos

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Q: Find the derivative of the inverse function to f(x)=ex-e-x

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Q: Find  y''  by implicit differentiation. 4x2 + y2 = 4

A: Given,  4x2+y2=y,we have to find y''Differentiate with respect to x,we get…

Q: f(x) = cos (x – a -2).

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Q: Find the derivative of the function. y = In(x8)

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Q: Find the derivative of the function. g(x) = In()x° – x|) %3D g'(x) = %3D

A: Formula used. ddxln(x)=1x;ddx(x)n=nxn-1

Q: Determine the derivative of f(x)=ln(x√x^2+1).

A:

Q: 18. If f (x) = es*, find (f-1)'(1) using Theorem 7 (Derivative of the Inverse Theorem).

A: We have to find derivative

Q: Find the derivative of the function. f(x) = 2x In(x) f'(x) =

A: Let us consider the given function as: fx=2xlnx By using product Rule of derivative, we get:…

Q: find the derivative of: f(x)= x^(1/x) using logarithmic derivatives

A: Given function

Q: Find the derivative of the function.

A: Given that, f(x)=ln(x-1)   As we know, ddxln(x)=1x Chain Rule Of derivative, If…

Q: Consider the function as folows:-   r(x) = 2x - 5 /(3x + 1)2 In general, how do you find the…

A: Given function: rx=2x-53x+12 We can write the function as rx=2x-53x+1-2 Differentiate the above…

Q: f(x) = x In x

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Q: Consider the function f(x) whose second derivative is f''(x)=4x+3sin(x)   If f(0)=3  and f'(0)=2…

A: detailed solution with explanation is given below

Q: 3/x +1 f(x) = X+2 at x = -1

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Q: Use implicit differentiation to find the 2nd derivative of x2 y + y2 x=-2

A: By using implicit differentiation to find the 2nd derivative of x2y+y2x=-2.

Q: Find the second derivative of the function.

A: Given the function: g(x)=x + ex  ln(x) We have to find the second derivative of the function. Let's…

Q: Find the derivative: 1+ e2x = cos 1 - e6x f(x) f'(x) =

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Q: Find the derivative of the function. f(x) = ln 2x/(x + 3)

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Q: Find the derivative of f(x) = e" – a3 +In(x) - In(x)

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Q: Find the derivative of the function. f(x) = 4 3√x + 2cos x

A: The given function is ; f(x)=4/3sqrt(x) +2Cosx.

Q: Find the derivative of the function. f(x) = 18 In(x) %3D

A: Derivative Question

Q: Find the derivative of the function. g(x) = 9 + In(x)

A: We have to find the derivative of : g(x)=ex29+ln(x)

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

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Q: Find the derivative of the function. f(x) 4. + 2cos x %3D

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Q: Find the derivative of the inverse function at x=1 for the function y=sin(x−1)+x2.

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Q: 3. ƒ : R+ → R, such that f(x) = √2x+2. (Hint: Apply the chain rule.)

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Q: Find the derivatives of inverse function: y = sec-1squareroot of 1 + x2 AND…

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Q: Determine the 8th derivative of y with respect to x of the function : f(x) = 1 / 1 + x2 and find the…

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Q: Q2) Use implicit differentiation to find y'" if y2 – 2x = 1 – y

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Q: 1) Find the second derivative of f (x) = 24 . %3D

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Q: Find y" by implicit differentiation. x² + 9y2 と y"

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Q: Find the derivative of g(x) = e-" cos(x²)

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Q: Find the second derivative of the function. f(x) = x x sin(x) %3D f "(x) - !!

A: Given:   fx=x sinx  To find: f"x=?

Q: Find y" by implicit differentiation. 3x" + 4y - 2

A: differentiate it with respect to x.

Q: Find the derivative of the function. x + 4 f(x) = In X – 4 | f'(x) =

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Q: Explain how to find a differential of a function.

A: Let us consider a function f(x) and its differential to be f'(x)

Q: Find the first derivative of g(x) = 2 In(x)tan(x*). g'(æ) = %3D

A: Given that g(x) = 2ln(x) tan(x^4). Find first derivative of this function. We know that derivative…

Q: Find all possible functions with the given derivative. = రx = 1x 2x

A: The answer is given below

Q: 2) Use the Chain Rule to express the second derivative of ƒog in terms of the first and second…

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

A: The function f(x)=lnx-3. We have to use the derivative to determine whether the function is strictly…

Q: In x g(x) = 2

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.