Sketch the graph of ƒ(x) = ln | x | and explain how the graphshows that ƒ′(x) = 1/x.

Q: Compute the derivative f'(x) for f(x) = log(x*) sin(x³).

A: Topic - derivative

Q: Find the derivative of f( x ) = 2° log3(z + 2.5) f'(x) =

A: The first derivative of the function is . The product rule of the differentiation is .

Q: g(x) = In tanh-1 x

A:

Q: Find F'(x) if F(x)= e^(-x^2) * x^(sin(x^3)) Use logarithmic differentiation

A: topic - logarithmic differentiation

Q: Without using a graphing calculator, how can I show the function 1-ln(y )= z in a graph and its…

A: Without using a graphing calculator,  Show the function zx,y=1-lny in the graph and its traces.

Q: What is the instantaneous rate of change of the graph of y = = cos x when x= 2n?

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Q: 4) Use logarithmic differentiation to find the derivative Of the given fünction.Show all steps.…

A: Consider the given function y=xx1+x24

Q: Evaluate the limit or derivative using properties of logarithms where x3 needed. dx x5+1

A:

Q: For x > 0, find f'(x) where f (x) = x**+3) via logarithmic differentiation. Show all of your work.

A: Use logarithm to solve

Q: In the function:  f(x)= (3x^2)ln(x) , x>0 What are the inflection points of the function?

A: To find inflection points of the function we need second derivative of the function.Use product rule…

Q: 3 7 - use logarithm differentiation to differentiate to find y prime (dy). y = x

A: The given function is, y = x.Take log on both sides of the function.

Q: 43. Find the function whose tangent line has slope (x + 1)e¯* for each value of x and whose graph X-…

A:

Q: 10 Find the derivative f'(0) of f(x) = at x + 4 x = 0 using the laws of differentiation.

A: Derivative of the function

Q: (A) Find an equation of the tangent line to the graph of f(x)=(4x+1)sin(πx) at the point whose…

A:

Q: Find y' by implicit differentiation. 1) x²y° = 2

A: Given equation: x2y9=2 To find: y' by implicit differentiation.

Q: 1 ソ= 1- x

A:

Q: (b) Sketch the graph of f (x) = ln(4 – x²). Use the first and second derivatives to identify where…

A: Consider the function  fx=ln4−x2

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

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Q: ) 1 = x* + 5y³

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Q: Find an equation of the tangent line to the graph of the function at the given point.

A: Here given function as y=log102xory=log 2xlog 10 Differentiate with respect to x dydx=log2xlog…

Q: )=1/x. Using this, compute the

A:

Q: Differentiate the following function.   y = ln(3x+1) - ln 3

A: We need to differentiate the following function.   y = ln(3x+1) - ln 3

Q: Differentiate the function   f(x) =    1/  ln x

A: Given function is fx=1lnx We know that 1an=a-n So, given function can be written as fx=lnx-1 Before…

Q: The graph of the derivative of a function is given. y For which x is the (original) function…

A: The graph of the derivative (f') of the graph f is given. Now, the original function f is increasing…

Q: What are the domain and range of ln x?

A: Given: y=lnx we know that in lnx, x>0 so, domain of given function is x>0

Q: compute the derivative g(x) = tan−1(ln x)

A:

Q: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y =…

A: given y=cos9θ+41

Q: Derermine The FirST derivative of : 千irsT OF F) = x³ .16 V5メ-2 こSioN Expa usiNG Logalith mic Ex…

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Q: True or False The graph of y = cos x is decreasing on the interval (0, π).

A: True or False The graph of y = cos x is decreasing on the interval (0, π).

Q: For x > 0, find f'(x) where f(x) = x*¯+3) via logarithmic differentiation. Show all ur work.

A: Topic:- application of derivatives

Q: The graph below is of f "(x) for some function f(x) with domain (-∞, ∞) (i.e., the graph of of the…

A: Since you have asked a question with multiple question in a single request, we would be answering…

Q: Use logarithmic differentiation to find for the curve defined by (r+1)"

A: Given,            x + 1y=y2x

Q: Find all the relative and absolute extrema of the given function on the given domain f(x) = x^2 +…

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Q: the first derivative of a continuous function y=f(x) is y'=x(x-12)^2 .find y'' and then use the…

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Q: Find an equation of the tangent line to the graph of the logarithmic function at the point (1, 0). y…

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Q: Find a number such that the tangent line to the graph y= log,(x) at x = a is parallel to the tangent…

A: The objective is to find the value of a

Q: X In Зх +1 y y' X

A: Given ; ln(x2/(3x+1))=y/x.

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

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Q: Find dx by logarithnic differentiation. (3x-2)(x"+3)

A: d(logx)/dx = 1/x

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: 6x = 4

A: Simple differentiation problem...

Q: What is the derivative of the exponential function a x, a >0 and a ≠ 1? What is the geometric…

A: The derivative of the exponential function ax is as follows.

Q: Using logarithmic differentiation, Show that y (x)= xa2" e®has no stationary points other than x =…

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Q: Use logarithmic differentiation to find the derivative of (x – 1)(x – 2) · · (x – n) - f(x) where n…

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Q: 1= x* + 5y3

A: The given equation is 1=x4+5y3

Q: Use logarithmic differentiation for find for y = (x-12)² dx x-8

A:

Q: Find the higher-order derivative. (4 log 2(x – 5)) dx2

A: Given, d2dx24 log2x-5

Q: 3. Use the graph of y = f (x) shown to sketch the graph of its derivative f'(x). [if on your own…

A: Give function f(x) has graph If you see this graph you will observe that derivative of f(x) will be…

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: