Q8.Letf(x) =In(t) It.%3D(6) Evaluathf'(10) = ?(b) Evaluata (f-Y (6) = ?%3D

Answered: Image /qna-images/answer/4361bcdf-a01c-4b67-94fe-49a353856594.jpg

Answered: Q8. Let f(x)= Ln(土) dt (6) Evaleata…

Math

Calculus

Q8. Let f(x)= Ln(土) dt (6) Evaleata f'(10) = ? (b) Enlnts (Fツ (o)=? (f-)) (6) =?

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section5.2: Exponential Functions

Problem 31E

See similar textbooks

Related questions

Q: Determine the instantaneous rate of change of the function πt ³ √x sin 2 f(x) = LV x3 1 + √t at x=2.…

A: Leibnitz integral rule.

Q: Q2 find the derivative of the following: 1) y = 2stn²(5x) ,2) y = Inx'n cosh 5x ,3) xsin¬14y = y…

Q: Find the differential of the function: y = x In x

A: Solution:Giveny=x ln xTo find the diffferentiationformula:(uv)'=uv'+vu'ddxxn=nxn-1ddxln x=1x

Q: What is the average rate of change of y = cos (2x) on the interval [0,π/2]

A: Given f(x)= y=cos (2x) to find the average rate of change over the interval (0,pi/2) average rate of…

Q: 31+2 dy - of the function y= dt 7. Find +4 dy of the function y = 5 tan (6x)+ log, (36x² + dx 8.…

Q: Find the differential dy of the given function y=extanx

Q: 7) Find the instantaneous rate of change of f(x) = ecos(z") + sin(In(8²)) at x = 1.

Q: Let y=(x2+3) to the 2nd power. Find the differential dy when x=4 and dx=0.2 ?????????? Find the…

Q: (a) Show that the derivative solution of this function y = x** is dy = x(**+x=1) [1+ x ln x (In x +…

A: The given function y=xxx Note: Multiple questions are given, we are answered with only one…

Q: 2. Estimate the instantaneous rate of change of y = at x = 1. Show your work. 2x-3x+1

Q: A particle is traveling upward and to the right along the curve y = ln x. Its x-coordinate is…

A: Given a particle is travelling upward and to the right long the curve y=lnx. It is given that dxdt=x…

Q: Find the differential d8y of the function y=exsinx.

Q: The derivative of y= sech-(Inx)+e sinh- (3x) equals Select one: +3esinh (3x) cosh(3x) y' = xlnxv…

A: The derivative of y=sech-1(lnx)+esinh-1(3x) is to be calculated by chain rule. The derivative of…

Q: 3. Water is being poured into a 10 liter leaky container so that the volume of the water, V,…

A: A differential equation is an equation that contains functions and their derivatives. A…

Q: How can I find the derivative of an integral. For example g(x)=the integral from 0-x (t+t^3)^.5 dt

Q: dy log x If xY = ex-Y, prove that %3D dx (1+ logx)?

A: Introduction :

Q: 1. Find the rate of y with respect to x at the point (1,8) if 7y² - xy³ = 4. dy dx

A: Given: 7y2-xy3=4 and Px,y=1,8 As we know that; The Power Law: ddxxn=nxn-1 The Product rule:…

Q: Evaluate the derivative of mq4.4.png cosh (bVx3 f(x) = a ln sinh(cx2) if a = 69, b = 0.6, and c = 6…

A: Given function: fx=alncoshbx3sinhcx2 To find: The derivative of the function f'(7) using…

Q: (e) Use a backward finite difference approximation to approximate the first derivative of the…

Q: Find the differential of the function y=xxe2x at the point x=1.

Q: Find the instantaneous rate of change of g(x) = In(x + 3) at x =

Q: = Determine the equation of the tangent line to the graph of f(x) = I x+ln x cosh (√2t - 1) dt at x…

Q: Compute dy/dx for the function. 5) y = In sinh 6x

A: topic- derivative of a function

Q: I. Find an equation of the tangent line to the graph of 1 t cosh (t² – 1) dt - f (x) = 1 tan-t 1+ln…

A: The given function is fx=∫1+lnx1tcosht2-1tan-1t dt.

Q: 1 log3(r – y)*

A: Given; fx,y=1log3x-y As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: 9. Find the derivative of the function using chain rule. f(t) = 3t In t

A: To find the derivative of the function

Q: 6) Calculate - dx for z = ln(x + y²).

Q: * find the dicredional derivative af the. f omc tion and in the direction of a= [o,3, 37 + find the…

Q: 7. Find dy and hence determine the rate of change of y with respect to x for the following…

Q: at x sin- 1 lim e J1 x→1 In x " 2 dt =?

Q: 1 By considering the secant through the points where x = 1.2 and x = instantaneous rate of change of…

Q: Find the linear approximation of f(x)=ln x at x=1 and use it to estimate ln(1.24). L(x)=?…

Q: 1. Find the derivative of the function:F(x)= [ (Vt arctan t)dt .

Q: (d) Compute the driectional derivative of f at (1,2) in the direc- tion u = (e) • point (1, 2)? What…

Q: 3. Find the derivative of f(x, y, z) = z2 + ye" at (In 2, 2, 1/2) in the direction in which the…

Q: A population x of rats satisfies the DE dx /dt ka?. Initially there are x(0) = 2 rats, and their…

A: The general solution of a differential equation always contains a constant of integration. The…

Q: -7/2 = 8. Calculate the derivative of y with respect to , if x/2 + y dy dx

Q: (e) Use a backward finite difference approximation to approximate the first derivative of the…

Q: (a) Find thẻ đéřivătivė. rivative. 1 y = In(x2 – 6) 3 dy dx (b) Find the derivative. 3 = INVX2 – 6…

Q: 2. ху 4 a. when x=8 10 dx b. when x-1 dt dy dt -6

Q: 2. If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y.

Q: Find the gradient of the tangent to the curve xy“ + y+ ( log_(x – 2))² = 14 at the point (3, 2).

Q: Determine the equation of the tangent line to the x³ + ln x graph of f(x) = sil 3 3 + 5tº dt at x =…

Q: The equation of the tangent line for the graph of Fx)= | Ln(P+4)dt at x=2 is F(x)=

Q: If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y. TRUE or FALSE ?

Q: A-The derivative is y = In Vsin 0 cos 0 1 + 2 ln 0

A: Let's find derivative of given function.

Q: Example2: Find the derivative of w=xy+z if x=cos t ,y=sin t &z=2t?

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

Q8.Let
f(x) =
In(t) It.
%3D
(6) Evaluath
f'(10) = ?
(b) Evaluata (f-Y (6) = ?
%3D

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 2 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

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

Repeat Example 5 when microphone A receives the sound 4 seconds before microphone B.
bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model P=20.913e0.0184t, where t represents the year, with t=1 corresponding to 2001. According to this model, when will the population reach 32 million?
A Troublesome Snowball One winter afternoon, unbeknownst to his mom, a child bring a snowball into the house, lays it on the floor, and then goes to watch T.V. Let W=W(t) be the volume of dirty water that has soaked into the carpet t minutes after the snowball was deposited on the floor. Explain in practical terms what the limiting value of W represents, and tell what has happened physically when this limiting value is reached.
The population, P, of the city of Hazelton has grown according to the mathematical model P = 65,000(1.075)*, where t is the number of years since 2005. a) At what percentage is the population growing? b) If this trend continues, during which year will the population reach approx. 100,000?
While rejecting H0 on a hypothesis test means that _______, measures of effect size tell you ______. how big an effect the treatment has; that the treatment has some effect that the treatment has some effect; how big an effect the treatment has that the treatment caused an increase; that the treatment caused a decrease d. that the treatment caused a decrease; that the treatment caused an increase
An efficiency study of the morning shift at a factory (7:00 A.M. to 12:00 noon) indicates that an average worker who arrives on the job at 7:00 A.M. will have produced Qunits t hours later, whereQ(t) = -t3 + 9t2 + 15tWhen during the morning shift does the worker’s production reach the point of diminishing returns?
Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY
Can you find the amount of salt A in the tank at any time t?
As baby boomers enter their golden years, the number of people afflicted with Alzheimer's disease is expected to rise dramatically. In a study published in the Journal of Neurology, the number of people with Alzheimer's disease in the United States age 65 years and over is projected to be N(t) = 0.00525t2 + 0.075t + 4.7 (0 ≤ t ≤ 4) million in decade t, where t = 0 corresponds to 2010.† (a)What is the projected number of people with Alzheimer's disease in the United States age 65 years and over in 2040? (Round your answer to four decimal places.) million (b) How fast is the number of people with Alzheimer's disease in the United States age 65 years and over projected to grow in 2040? million per decade (c)How fast is the rate of growth of people with Alzheimer's disease in the United States age 65 years and over projected to change in the period covered by the study? million per decade per decade
The analysis of tooth shrinkage by C. Loring Brace and colleagues at the University of Michigan’s Museum of Anthropology indicates that human tooth size is con-tinuing to decrease and that the evolutionary process has not yet come to a halt. In northern Europeans, for example, tooth size reduction now has a rate of 1% per 1000 years. a. If t represents time in years and y represents tooth size, use the condition that y = 0.99y0 when t = 1000 to find the value of k in the equation y = y0 ekt. Then use this value of k to answer the following questions. b. In about how many years will human teeth be 90% of their present size? c. What will be our descendants’ tooth size 20,000 years from now (as a percentage of our present tooth size)?
Note in the model y(hat) = 2 + 3x1 - 1x2 + 2x1x2 B1 (hat) =3. is it appropriate to say that we expect the response y to increase by 3 when x1 increases by 1 unit? why or why not?