Estimate the instantaneous rate of change at the point x=2 for f(x)=ln(x) ROC =

Q: y = (In x)* xln x

A: Explanation of the answer is as follows

Q: Determine the first derivative of the ff. function y = tan(ln(cot(x² + 3 ln 3x)))

A: Chain rule of differentiation: f(g(x))'=f'(g(x))g'(x) Formulae used: ddxtanx=sec2xddxlnx =1xddxcot…

Q: Find the derivative of the logarithmic functions: y = ln (tan^2 θ )

A:

Q: 11. y=3x+ ln x %3D

A: Topic - derivatives

Q: What is the rate of change of y = ln x at x = 10?

A: To find the rate of change we have to find dy/dx

Q: Find the derivative of Log(2z³). 2/z 2/2? 1/2? 3/z

A: Answer

Q: Estimate the instantaneous rate of change at x=2

A: Please refer to the image below

Q: Find the derivative.

A:

Q: kel derivative

A:

Q: 2. Show a graphical method of approximating the instantaneous rate of change at x = 3 for the…

A: You must have idea about what is the basic difference between instantaneous and average rate of…

Q: Estimate the instantaneous rate of change of P(x)=5/x+2 at the point x=2

A:

Q: 11. Use logarithmic differentiation to find the derivative of the function. y = xsinx

A:

Q: 2X Y=ln (3") +sec (Inx)+tan (ln5x)

A: We will differentiate the function and simplify.   The detailed solution is as follows below:

Q: If the instantaneous rate of change of ƒ(x) with respect to x is positive when x = 1, is ƒ…

A:

Q: 3. Use logarithmic differentiation to find the derivative of y with respect to the given independent

A: Part a,Given,           y=x2+1x-12

Q: Find both the derivative and indefinite integral of ƒ(x) = 4 cosh 2x.

A: Here given as ƒ(x) = 4 cosh 2x. Thus

Q: 5th derivative of y = log x^5 to the base 2

A:

Q: Compute for the derivative of the function using logarithmic differentiation g(y) =…

A: Logarithmic differentiation: - The use of logarithms to derive the derivatives of some difficult…

Q: f (x) = ln(x · 5*)

A:

Q: 2. Use logarithmic differentiation to find first derivative of y (sinx)r

A: Formula used: ddx[u(x)v(x)]= u(x)v(x).ddx[ln(u(x)).v(x)] ddx(u.v) =dudx.v + udvdx

Q: A bicyclist is riding on a path modeled by the function f(x)=0.04(8x-x^2) , where x and f(x) are…

A: Given path functionfx=0.048x-x2

Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

A: y = (lnx)lnx Take log to the natural base e on both the sides to get,

Q: Y sinh(1) (use logarithmic differentiation) 3 (sec x)²/2[/cot-¹x]

A:

Q: This is determined by the largest derivative, or the highest level of differentiation, present in a…

A: We have to check

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

A:

Q: Find the rate of change of f (x) = x° at x = 2. %3D

A: Rate of change.

Q: Find and sketch an exponential equation of the form y = Ce^kx that passes through the points (0,8)…

A:

Q: Find the second derivative of the function. g(x) = √x + ex ln x

A: Consider the given function gx=x+ex lnx Now, differentiate the given function with respect to x…

Q: what is the derivative of f(x)=ln(tanhx)

A:

Q: Find the derivative of y = log2 4x Ox/In4 O 1/xln4 O4/1n4 @ 4/xin4

A: To solve the following problem

Q: 1. Use logarithmic differentiation to find first derivative of y = xsinx

A: As per our company guidelines we are supposed to answer only first question. Kindly repost other…

Q: Find the instantaneous rate of change of y =- at x = a

A:

Q: What is the derivative of: log x/(x+1)

A:

Q: Find the equation of the line tangent to the graph of y = 6 ln(x) at x = 3. Tangent Line: y =

A: We have to find the slope of tangent at first.

Q: Find the derivative. y =(ln(ln x))3

A:

Q: Find the slope of the tangent line to the exponential function at the point (0, 1). y (0, 1) 1

A: Tangent to a curve is a line which just touches the curve and in some sense is parallel to the…

Q: wwww To find the slope of the tangent line to y = ln(x²) at the point (1,0) we must find the…

A: Recall: Slope of the tangent line

Q: Find the nth order derivative of the natural logarithm function y=lnx.

A:

Q: compute the rate of Change of the functioN at x= a. flx)= -2X²-X,Q= -5 instantaneous

A: Given function: fx=-2x2-x

Q: gives a good approximation, where t is time in years since 2007. Find the derivative function R'(t).…

A: The model representing the given data is defined by the function Rt=0.25t2-t+29 gallons, where…

Q: Find the derivative. y(x) = x tanh−1(x) + ln (sqrt (1-x^2))

A:

Q: use logarithmic differentiation to find the derivative of the function fx)=(sinhx)s(sx)

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

Q: 11. Use logarithmic differentiation to find the derivative of the function y = xsinx

A: Given function is : y=xsinx To find the derivative.

Q: calculate the derivative y = sinh(ln x)

A:

Q: Determine the equation of the tangent line to •x³ +ln x the graph of f(x) at x = 1. [² = √/3 + 5t5dt

A:

Q: What is difference between the derivative of log(sin(x)) and the derivative of ln(sin(x))?

A: The difference between ln and log is the base of ln is e and the base of log is 10

Q: 3. Use logarithmic differentiation to find the derivative of the function. (2x – 1) Vx+1 y =

A: giveny=(2x2-1)5x+13taking log on both sidelogy=log(2x2-1)5x+13using log…

Q: Find the derivative of s(*) - L Int dt 1+t

A:

Q: 6. Use the difference quotient to estimate the 2 instantaneous rate of change in f(x) = x² at x=3…

A:

Exponential Growth Model

The relation that represents an exponential function is: