Please solve all steps, thanks!! Find the derivative of the logarithmic function.In3xx+ 2,f(x) = InStep 13xRewrite the given function, (x) = In-). Apply the logarithmic property, In== In a-v In b.Thus,RM) = In() = In(3|D-In(x+).

Answered: Image /qna-images/answer/8e0e35ef-8d30-487e-8304-9c4d9be2be27.jpg

Answered: Find the derivative of the logarithmic…

Math

Calculus

Find the derivative of the logarithmic function. 3x f(x) = In %3D x+2,

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter4: Exponential And Logarithmic Functions

Section4.3: Logarithmic Functions

Problem 5E: The natural logarithmic function f(x)=Inx has the ____________ asymptote x =____.

See similar textbooks

Related questions

Q: D. e ind the Residues of function

A: The given function is ez-1z To find residue we first calculate and classify singularities of the…

Q: Find a positive number a such that the sum of its reciprocal and 5,324 times its square is as small…

Q: Mary Katherine has a bag of 3 red apples, 5 yellow apples and 4 green.apples. Mary takes a red apple…

Q: Determine the equation of the plane that contains the points P=(1,-2,0) P=(1,-2,0), Q=(3,1,4)…

A: Here we have to determine the equation of the plane that contains the points P(1,-2,0), Q(3,1,4) and…

Q: 6. Use identities to show the following statements are true. sin x cos x tan x =1-cos?x a) b) ,sin x…

Q: Evaluate the integral. 4 f(x) : 16 – x2 if -4 < x < 0 0 < x < 4 f(x) dx where if

Q: The double integral

A: answer is in step 2

Q: EXERCISES 5: Find equations for the (a) tangent plane and (b) normal line at the point Po on the…

Q: Find the derivative of the logarithmic function. y = In 6 + e 6- e*. Step 1 The given function y =…

A: We will derivate the function step wise as asked in the question.

Q: 78 |x cos(nx)dx

A: As per guidelines we will solve one question

Q: Use the requested method to approximate the definite ir Use the method of left Riemann sum with n =…

Q: 2л 67 xsin 3xsin 2.xdx

A: You have asked multiple questions and not mentioned about which question answer you need so…

Q: Consider the following. (If an answer does not exist, enter DNE.) h(x) = 5x3 - 3x5 %3D (a) Find the…

Q: y=(x+5)^x Differentiate

A: Solution: y=(x+5)^x dydx=ddx((x+5)x)

Q: Given the function f(x) 3x? f(x + h) – f(x) Find the difference quotient -3(h + 2x) f(x + h) – f(x)…

Q: A company is constructing an open-top, square-based, rectangular metal tank that will have a volume…

Q: Q1/ Using newton's backward difference fomula find the approximate value of y(-1/3) when y(-0.75) =…

Q: 1. f o" xy dy dx О а. 32/3 ОБ. 16/2 Ос. 32/4 O d. 18/4

Q: The graph of a function f is given. 10 Estimate f(x) dx using five subintervals with the following.…

Q: Find a power series representation for the function. (Give your power series representation centered…

Q: Find the derivative of the function. 6x3 + 8x2 f(x) = Step 1 The function f((x) can be simplified to…

A: We have to find the derivative of the given function.

Q: opportunity loss will always result the same decision as maximum Expected value ? 2-Prove…

A: 1) Expected Opportunity Loss = EOL Expected Maximum Value = EMV FOR PROVING , Let Regret Table :…

Q: f(x) = b (for some 1 b > 0) at any point on the curve The distance between the r-intercept of the…

Q: Consider the function f(T,y)= kr - 2xy + y?. %3D 1. Show that (0, 0) is a critical point of f(T, y).…

Q: The series n=4 is convergent. The term a29 of the sequence {a,) given by 2 3 4 5 5'7'9' 11 is 31 63…

Q: If 0 = 3 then sin(0) = %3D cos(e) = %3D Give exact values. No decimals allowed! Question Help: Video…

A: Given that θ=-1π3To compute sin (θ) and cos(θ)Now , sin(θ)=sin(-1π3)=-sin(1π3)…

Q: Find an equation of the tangent line to the curve at the given point. y = sec(x) – 2 cos(x), P = 1 3

Q: y = sin æ , y = cos(2x), – < < 6.

Q: 22. On what value of x is f(x) = x2+3x-10 has %3D x-2 removable discontinuity? A) 5 B) -5 C) 2 D) -2…

Q: 4 8 Suppose the sequence {b1, b2, b3, ...} is given by {-1, , 9' 27 Which, if any, of the following…

Q: Divide and simplify. 4nº – 28nº + 16n? 6-28n° - 4n4 4n -28n5+ 16n2 n4 - 7n3 +4 (Simplify your…

A: Divide and simplify

Q: Given the differential equation y' = 4y2 + 7 Take the Implicit Derivative of this function 2 times…

A: Consider the equation y'=4y2+7

Q: Consider the parametric equations below. x = t2 − 2, y = t + 3, −3 ≤ t ≤ 3 (a) Sketch the…

Q: Find the gradient of the function at the given point. g(x, y) 6xey/x, (1, 0)

Q: A manufacturer can produce at most 100 units of a certain product each year The demand equation for…

Q: 0. Find the dimensions of a rectangle of maximum area that can be inscribed in a circle of radius 4…

A: Given: radius ( r ) = 4 cm

Q: Consider the equation below. = 9 cos2(x) – 18 sin(x), 0 < x < 2n (a) Find the interval on which f is…

Q: to 4y" – 25y = 0

Q: I. Evaluate the following. 3450°-j12 a. 14 + j2 – -j15 (3450°-j12) b. j2 x 32-25° -j15 5-j2…

Q: Determine the convergence or divergence of the series. (If you need to use co or -00, enter INFINITY…

Q: Liaed the Residuesof fucation coske)

Q: = 8x - 3y2 nd the Implicit derivative " dy/dx" of the function. A) y' = - 6y B y' = 8 - 6y (Cy' -6y…

Q: x 4 kx + 3, а. Let g(x) = 8, a) Find the value of k if g (x) is continuous at x 3. b) Determine…

A: Solving

Q: Given the differential equation y' = 6 x y and y(0) = 10 and its next few implicit derivatives y" =…

Q: A scientist has discovered a new strain of bacteria. The bacteria culture initially contained 1,000…

A: Given problem:- A scientist has discovered a new strain of bacteria. The bacteria culture initially…

Q: Consider the following function. f(x) = |x - 3| %3D Find the derivative from the left at x = 3. If…

Q: 10. Determine whether the improper integral converges or diverges 3 dx (x – 1)/

Q: III. Graph the following functions: 4. y lIn(x-3) 5. y= In(x-1) 6. y= In Vx-1

A: Consider the functions 4. y=|ln(x-3)|5. y=lnx-126. y=lnx-1

Q: Find the slope of the tangent line to the graph of the function at the given point. g(x) = 14 – x;…

A: Use. Slope formula for finding the value

Q: 1. Use the definitions of the hyperbolic function to find each of the following limits. sinh(x) lim…

Question

Please solve all steps, thanks!!

Find the derivative of the logarithmic function.
In3x
x+ 2,
f(x) = In
Step 1
3x
Rewrite the given function, (x) = In-). Apply the logarithmic property, In=
= In a-v In b.
Thus,
RM) = In() = In(3|
D-In(x+
).

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 with 3 images

SEE SOLUTION Check out a sample Q&A here

Similar questions

If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per second. What is the terminal velocity, and how long does it take the filter to reach 99 of terminal velocity? Use a table increment of 0.1 and given your answer to the nearest tenth of a second.
The natural logarithmic function f(x)=Inx has the ____________ asymptote x =____.
Find the derivative of the logarithmic functions: y = ln ( 4x^3 - x^2 + 1^2)
find the derivative of the log functions: y = ln(x√x2 – 6) f(x) = ln(2x/x+1) y=ln(suqared root of x+2/x-2
Give the derivative formula for the function. f(x) = 2x−3 + ln(3)
Compute the derivative in terms of log for y=log(xe^(-3x))
use logarithmic differentiation or the method to find the derivative of y with respect to the given independentvariable. ey = yln x