Let h(x)=f(x)/g(x), where f(x)=ln(3x2 +2x+2) and g(x)=−2x. What is h′(x)?

Q: Find the value of the derivative (if it exists) at the indicated extremum. (If an answer does not…

A: Find your answer below

Q: find f'(x) of (((3x^2+1)e^x^2)/(2x+1)^5)^5 using logaithmic differentiation.

A: The given function is,

Q: Find the differential of the function y=(3-x8)1/2

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Q: Find the derivative of the composite natural exponential functions 1. f(x) = In( 2. g(x) = In(v³ +1)…

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Q: then find f(x). | f(x)dx = = ln([x]) In(x) - sec(x) - 4e + 2 -x + 6x + C

A: The integration of f(x) equal to the;  ln(|x|)-sec(x)/3 -4ex/4+x2/2 +6x +C.

Q: Compute the indicated derivative. d + 7x)(x2. dx x = 2

A:

Q: Find dx * for y = (x² + 2)°(1 – x³)* using logarithmic differentiation.

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Q: Use the u-substitution to find the anti-derivative of m'(x)= 1/xln(x)

A: solution :- antiderivative is the integration  So put ln(x)  = u Then (1/x )dx  = du And then…

Q: What is the value of ln[f'(2)] if f(x) = e^x?

A:

Q: y = (e*+4 +2)/(e2+3x +1)

A: y=e-3x+4+2e2+3x+1

Q: Find the first derivative of the function g(x) = V5 +x +4cos (2x).

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: Find the derivative of f(x)=x^2 e^2.5x

A: Given problem:- Find the derivative of f(x)=x2 e2.5x

Q: Find the derivative y = (2x – a) (x² + e-")

A: We havey= (2x-x3)(x2 + e-x)

Q: Givenf (x) = ln x, what is the derivative function f' (x), and what is its domain? f' (æ) = e², for…

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Q: What is the first derivative of f (x) = ln n A)? 3x²+7x 5х Select the correct answer below: бх-7 O…

A: Given query is to find the derivative of the expression.

Q: Find the second derivative. 1 h(x) = x2 %3D | h"(x) = %3D

A:

Q: 5. Use the chain rule to find the derivatives of (a) y = log; V4 + 1 (b) y = (x – e-")²

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Q: b) Find the derivative function of f(x) = √5x - 1 using first principles.

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Q: S-2(x-1 - x²) dx 5.

A:

Q: Find the finite derivative of a the functions below at x=1: a) f(x) = 4x³-3x²+2x-3 3 b) f(x)==-²/ 3…

A: Concept: The derivative can be represented as f'(x) or ddx(f(x)) Derivative of xn: ddx(xn)=nxn-1…

Q: Find the first derivative of: x = t²e2t

A:

Q: 1. Find the derivative of the function f (x) = e2x + 5* + x3

A:

Q: Find the derivative of the function y = In(8 – e-a f'(x) =

A: We have to find derivative

Q: e3x-e-3x Y = e 3x+e-3x 4. t2 y= 72-1 5. X = t-1

A:

Q: Find the second derivative of the function. f(x) = (3 + 2x)e−3x

A: Given:The given function is f(x)=(3+2x)e-3xTo find:The second derivative of function f(x)

Q: h(x) = e(-1/2)x

A:

Q: Find the derivative of f(x)=(x+4)e^(5x)

A: We have to find the derivative of f(x) ,where f(x) is given by

Q: Find the derivative of y with respect to x. y= sin -3 O A. XV1-x - 3 O B. 1+x - 3x 3 c. 1-x -3 O D.…

A: Given that: y=sin-11x3

Q: In(r) Find dy/dx using the method of logarithmic differentiation when y = (4+ 2x²).

A:

Q: The derivative of In x is and the derivative of a constant C is, sO X dx = In |x| +C for x> 0.

A: Given x>0, The differentation of natural log x is 1/x  And differentation of constant are zero.

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 y with respect to x. y=x* In (x) - O A. x* In (x) - x² + 5x* O B. 6x -x OC.…

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Q: h(x) = (cos x)(4x²– 3)

A: Explanation of the answer is as follows

Q: For the function f(x) = 3x ln x, find f'(x) =

A: Given functionfx=3x4 .ln x

Q: 1. Find the anti-derivative of the following. e" (x + 1) dx x2

A: From the given information. Anti-derivative has to be calculated to the following expression.

Q: Find the first derivative or f'(x) of the function below using the techniques of integration f (x) =…

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Q: Find the inflection points of the function f(x) = x 2 ln x

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Q: h(x) = In (2x-2)+(x² +1)e³x-6 %D Calculate the derivative at x=2, that is h'(2)=

A: calculate the derivative as shown below: h'x=ddxln2x-2+x2+1e3x-6…

Q: Find the derivative of f(x)=(x−2)e^(−3x).

A: The first derivative of the function f(x) = (x−2)e−3x is calculated as follows.

Q: Solve for the derivative of the given functions using the Chain Rule formula. Let f(x) = √(x2 + 3x +…

A: (a) fx=x2+3x+1 Inner function : u=x2+3x+1. Outer function : y=u.

Q: Find the derivative of h(x) = e³ + Vx + lnx. I

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Q: dx = +C (x+1)² X+1

A:

Q: Find the derivative of y. x2 =log6 x+1 O A) Sx+1 x2 O B) ) In 6 x2 2x+1 1 Sx+1 In 6 x2 D) None of…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the first derivative of g(x) if g(x) = e²* In(2x) %3D

A:

Q: Find the derivative of f(x)=

A: We use the quotient rule of logarithm to simplify the expression

Q: Find the derivative of the given function e5x (2x+1)5 b. f(x) = In Vx²+1 f(x) = (x In x – x)

A: Given that: b. f(x)=lne5x(2x+1)5x2+1c. f(x)=(xlnx-x)

Q: nd the derivative of the function  h(x)=ln(4x^2+3)

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Q: Find the anti-derivative of g'(x)= log1/2(X)

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Q: Find the derivative of the given function. e5x (2x+1)5 f(x) = In Vx2+1

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Q: Find the derivative of the function f(x) = 3 ln(x) + e5ª. df = dx

A: