Derivatives of logarithmic functions Calculate the derivative of the following functions. In some cases, it is useful to use the properties of logarithms to simplify the functions before computing ƒ′1x2.  y = log10 x

Q: 3. (a) Use logarithmic differentiation to show why the derivative of a is a In a, where a is a real…

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Q: Derivatives of logarithmic functions Calculate the derivative of the following functions

A: Given function is y = log8tan x. From Property of logarithm, we have loga b  = ln bln a Therefore,…

Q: 2 Example 36: Find the derivative of log, x by ab-initio method. A Example 36: Find the derivative…

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Q: 1+4 In(t) f (t) = 5t3

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Q: Derivatives with general logarithms Compute the derivative of the following function

A: We use the change of base property of log. Then we use the chain rule of the derivative.

Q: MJM) Using logarithmic differentiation find the gradient of the tangent to the curve represented by…

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Q: Derivatives of logarithmic functions Calculate the derivative of the following functions

A: To find: The derivative of y=1log4x. Concept used: Logarithmic power rule: ln ab=b·ln a Chain rule…

Q: Derivatives of logarithmic functions Calculate the derivative of the following functions. In some…

A: Here This can be written as

Q: The process of finding the derivative of a given function is equivalent to a. determining the…

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Q: An unknown function's derivative is h'(x) = 3x-2 - 6. Using your understanding of the derivative…

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Q: a. Find the derivative function f for the following function f. b. Find an equation of the line…

A: Given : fx = 4x2-12x+1

Q: Logarithmic Differentiation. Determine the derivative of the following functions.

A: f(x) = 2-csch(2x). (ln x)x Now we use chain rule (uv)' = uv' + vu' put v = (ln x)x        ln v = x.…

Q: 19. + Question Details Use logarithmic differentiation to find the derivative of the function.

A: To find the derivative of the composite function , using logarithmic differentiation

Q: Find the derivative of the function. (a) g(x) - log,(8x - 9x²) - (x),6 (b)

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Q: Derivatives Find the derivative of the following functions for the derivative of√ x . g(x) = e3

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Q: Derivatives of logarithmic functions Calculate the derivative of the following functions

A: y=log2(log2x)

Q: Find the second derivative f"(x) for f(x) = e5-3, Hints: First find the derivative of given function…

A: Given: f(x)=e5x2-3 To determine: Second derivative of the given function.

Q: Derivatives of logarithmic functions Calculate the derivative of the following functions. In some…

A: Given: y=4log3x2-12. for find derivative of it we first change base of log into e for that we will…

Q: 1. f(x) = Vx

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Logarithmic Diffetentia tion Use logarithmic differentiation te find the derivativeof Hwith respect…

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Q: Logarithmic Diffetentintion Use logarithmice differentiationte find the derivative of Hwith respect…

A: Solution  using log property,

Q: A Function and Its Derivative Which of the following functions are their own derivative? y = e* + 4…

A: a) Given function: y=ex+4 Differentiate the above w.r.t 'x' y'=ddxex+4y'=ddxex+ddx4y'=ex+0y'=ex

Q: e* (x+2)' /3x-5 Use logarithmic differentiation to find the derivative of the function. f (x) = -3x

A: Given, fx=e-3xx+253x-56 Let y=fx ⇒y=e-3xx+253x-56⇒y3x-516=e-3xx+25 Taking logarithm on both sides…

Q: Derivatives with exponentials Compute the derivative of the following functions.

A: Use the two rules given as follows: The derivative of a composite function is fgx is f'gx·g'x. The…

Q: Derivatives of logarithmic functions Calculate the derivative of the following functions. In some…

A: Given: f(x)=ln 10x To determine: Derivative of given function using property of logarithms.

Q: Find the derivative of the function and evaluate the derivative at the given value of a. X = (x)4 ;a…

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Q: a) Complete the differentiation rule: In x. b) Complete the differentiation rule for b > 0: log, x.…

A: a. Rule for ln(x) is below:

Q: Question Find the derivative of f (x) = log, (4x* + 3x) at the point .x 1. %3D Enter an exact…

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Q: Find the derivative of the function below. Do not simplify your answers (SHOW ALL STEPS) f(x) =…

A: Given the function f(x)=(log2(3x+1))4+5x

Q: Find the derivative of the function below and simplify the result.

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Q: Derivatives of logarithmic functions Calculate the derivative of the following functions. In some…

A: Derivative: y=log8|tanx| logab=lnblnay=log8|tanx|  =ln(tanx)ln8

Q: F. (DERIVATIVES OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS) 1. Find f'(x) if f(x) = 3e². 2. Find g'(x)…

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Q: x³sin?xcosx Find the second derivative of the function f (x) e-X(x-1)x

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Q: Derivatives of logarithmic functions Calculate the derivative of the following functions. In some…

A: Given- y=1log4x To find- The derivative of the above expression. Identity Used- logmn=loganlogam

Q: CURRENT OBJECTIVE Use logarithmic differentiation to find a derivative Question Find the derivative…

A: We need to evaluate the given derivative. The given function is in the form f(x)^(g(x))

Q: y = log(x – 3) (x+ 3)5

A: y=log(x-3)5(x+3)5

Q: a. Find the derivative function f' for the following function f. 5. Find an equation of the line…

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Q: 6. Find the derivative of the following function. You may want to use logarithmic differentiation.…

A: Explanation of the answer is as follows

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

A: we have to find the derivative of the following

Q: (a) Find the derivative. dx (b) Find the derivative. y = In - 5) State whether the function in part…

A: Given :         a)      y=13lnx2-5b)      y=lnx2-53

Q: 1. y=x(VT- x³ )

A: As we know that; The logarithmic rule: 1).loga·b=loga+logb2). logam=mloga The exponent rule: aman…

Q: V4+ x2 g(x) = In

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Q: 39-50 Use logarithmic differentiation to find the derivative of the function. 39. y = (x² + 2)²(x* +…

A: • For finding derivative using Logarithmic differentiation, we have to take logarithm both sides and…

Q: Use logarithmic differentiation to find the derivative of the function. X - 5 y = x° + 5 .8

A: Use logarithmic differentiation to find differentiation of the function: y=x-5x8+5

Q: Int g(t) = t2

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Q: Logarithmic Diffetetintion Use lagarithmic differentiation te find the derivative of «with respect…

A: As per our guideline we are allowed to do 1 question or 3 subparts at a time. Please post other…

Q: Logarithmic Diffetentiation Use logarithmic differentiation te find the derivative of with respect…

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Q: Find the derivative of the function. g(x) = log7(x) g'(x) =

A: We have to find out the derivative of the function g(x) = log7(x)

Q: g Ca) : -8) (uring logarithmic differentiation) 2 +4 11

A: We can find the derivative using logarithmic differentiation as below.

Q: Find the derivative of the inverse of the following function at the specified point on the graph of…

A: SOLUTION-

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: