Answered: The general anti-derivative of the…

Math

Calculus

The general anti-derivative of the function f (x) - In(x) is given by x In( x)+ C Inx)-x+ C x In(x) - x +C xlnx) +x+C

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Q: Find the derivative using the theorems on derivatives. dx x2-2 1 y = 2.y = (x² – 1)³(x² + 3)² x3+4x…

A: Given functions to be differentiate are 1. y=x2-2x3+4x 3. y=x2-2x we will make use…

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

Q: Find the derivative of a function at a certain number using the formula f(x) – f(x1) x-X1 x- x1…

A: Here's the solution, please have a look at it...

Q: Determine the derivative of f(x) = 3 x2 In x with respect to x. f '(x) :

A: We differentiate both sides with respect to x and apply the rule d/dx(uv)=ud/dx(v)+vd/dx(u)

Q: Find the derivative of the function. 3 In (x +8) 5-5x O A. dy %3D dx (x + 8)(5 – 5x)? О в. dy 15 -…

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

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

Q: a. Find the derivative of f(x) = x2 - 5x at x. That is, find f′(x). b. Find the slope of the tangent…

A: Given: fx=x2-5x To Find: a. f'x=?b. Slope of tangent line of the given function at x=-1 and x=3

Q: Find the derivative of the function. f(x) = In(x + 1) f'(x) =

A: To find the derivative of the function fx=lnx+1

Q: What is the derivative of f(x) = %3D (² - (z – 1)")* 02 (2 – (a – 1)°) (-3z² + 8z – 3) O2 (2² - (2 –…

Q: Determine the derivative of f(x) = 3 x² In x with respect to x. f'(x) = |

A: We have to find f'(x)

Q: f(x) = cos (x – a -2).

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…

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: 7) f(x) = 3e In x %3D

Q: 2. Let f(x) = x² ln x + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D

Q: Find the derivative of function.

Q: find the derivative of f (x) at the designated value of x. f (x) = x3 at x = 12

A: The derivative of a function can be calculated by differentiating both sides of the function with…

Q: Find the anti-derivative of g(x) = sec(x) tan(x) which contains the point (TT, 0). O G(x) = -csc(x)…

A: Solution to the anti-derivative can be found by integrating the function.

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

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: Find sixth order derivative of the function f(x)=(x-5)^7.cos(5x) by using Leibnitz theorem.

A: n! = n × (n-1) × (n-2) × (n-3) × (n-4) × ............ × 1

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) =…

Q: find the derivative of f (x) at the designated value of x. f (x) = x + 11 at x = 0

A: To find the derivative of f(x)=x+11 at x=0 Solution: f(x)=x+11 Differentiating both sides w.r.t x we…

Q: Give a value for c that satisfies the conclusion of the Mean Value Theorem for Derivatives for the…

Q: Find the derivative of y with respect to x, t, or 0, as appropriate. 1-x y = In (x + 2)5 4x - 7 (x +…

Q: 2. Let f(x) = x² In a + 1. Use the second derivative formula to approximate f"(1) when h = 0.2. %3D…

A: Given that, f(x)=x2ln x +1 To find f''(1) when h=0.2 Using second derivative formula,…

Q: Shows the derivative function of: u³ + 2u, where u = x² + 3

A: Let's find.

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) =…

Q: if f(x) = x²√√In x² P x A. f'(x) = . find the derivative of this function f'(x) 1-In x² x²√√In x²…

Q: Find the derivative of y with respect to x. 1, 1+x2 In 1- x3 y

A: If you have function f(x) in the numerator and the function g(x) in the denominator, then the…

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: 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) = 4x2 – 13x – 30 by definition of derivatives f(x + h) –…

A: We have to find the derivative of the given function: fx=4x2-13x-30 by the definition of…

Q: Find the derivative of the function. InV y = In 6 - X %3D y' = %3D

A: Explanation of the answer is as follows

Q: Let y be a function of x and suppose y= In(y-x). What is the correct result for the derivative of y…

Q: Compute the derivative of f(1) = In(x In(x² In(r³))).

A: The given function f(x)=lnx lnx2 lnx3

Q: Find the derivative of the function. 92-4x + h(x)= e 18x – 4x2 –1 92-4z++ x2 O b. 9x - 8x² – 1…

Q: The derivative of the function f(x) = 5+ ln r is: 1 a. f'(x) = 2.x/5+ In x b. f'(x) = 2/5+ In x In x…

Q: Find the derivative of f (x) = coth³(1In(x³)). %3D A 9x²coth?( In(x³)) csch2(In(x³)) - 9coth (…

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

Q: Find sixth order derivative of the function f(x) = (x – 5)7.cos(5x) by using %3D Leibnitz theorem.

A: If y=uv where, u and v are functions of x then un and vn denote the nth derivative of u and v with…

Q: Find the most general anti-derivative of f(x) = 9/x +1+ co x. %3D 9/x- sin x + C 6xVx + x +sin x 6xV…

A: Here I am attaching image so that you understand each and every step.

Q: 2. Determine the 8th derivative of y with respect to x of the function 1 f(x) = 1+x2 and find the…

A: Taylor series

Q: Find the derivative of the transcendental function. h(x) = 7e cos x h'(x) = %3D

Q: 5. Find derivative of the following composite function using the Chain Rule: f(x) = 3x2 + 8x, x(t) =…

Q: the function f(x) = In 5x +3x + 13). 6. Differentiate ° 7. Find the derivative of the function .2 y…

Q: Find the derivative of f with respect to x of f(x) = In x'

Concept explainers

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.

Question

Thanks.

7.
The general anti-derivative of the function f (x) - In(x) is given by
x In( x) + C
Inx)-x+ C
x In(x) - x +C
xin(x) + x +C

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Point Estimation, Limit Theorems, Approximations, and Bounds$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions

Suppose that the first derivative of y = ƒ(x) is y'= 6x(x + 1)(x - 2). At what points, if any, does the graph of ƒ have a local maximum, local minimum, or point of inflection?
2) Find the derivative of g(x) = 4x^2−3x+5 using the limit process.
11) Find an anti-derivative for each function in C equals zero
What is the value of the first order derivative of the closed function given as x3+y3+3xy+3y2+6x+6y=0 at the point x = 1 ?
FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM ( 1. y = Arctan√3x−4/4 2. y = 2 Arccos ( 1 -x/2) + √4x − x2 3. y = ln (x3(x−1)/(x−2)^2) 4. y =e^3x−e^−3x/e^3x+e^−3x 5. x =t/t−1, y =t2/t2−1
When the Second Derivative Test Fails Analyze the critical points off (x, y) = 3xy 2 - x 3 .
What is the numerical approximation of the derivative of the function f(x) = x^3 - 2x + 1 at x = 2 using the forward difference formula with a step size of h = 0.1?
Find the partial derivative with respect to x of e^y-2*ln(x)-x^3y^2.
If ƒ(x) = xn, n ≥ 1, show from the definition of the derivative that ƒ'(0) = 0.
Find the derivative of: y = 4x^2 – 1/x y’ = 2x – x^(-2) y’ = x^(-1) + 8x y’ = 8x - x^(-2) y’ = x^(-2) + 8x None of the above
What is the approximate value of the derivative of the function f(x) = 2x^3 - 5x^2 + 3x at x = 1, using a forward difference approximation with a step size of h = 0.1?
1) Calculate the derivative of f1 (x) = (2x + 3) / (x - 5) using the definition of the limit of the rate of variation. 2) Calculate the derivatives of the following functions