What is the value of ln[f'(2)] if f(x) = e^x?

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 )

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Q: Find the derivative of f(x) = COS 4 log3 (x²) os(5x)

A: Explanation of the answer is as follows

Q: Suppose we want to use logarithmic differentiation to calculate the derivative of y=x²x . As a first…

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Q: Find the derivative. h(x) = In(cosh(7x)) h'(x) =

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Q: What are the formulas for differentiation and integration?

A: Differentiation formula: There are many formula available in differentiation. few of them listed…

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: What is the derivative of 2(x)ln(x)+x

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Q: Compute the derivative in terms of log for y=log(xe^(-3x))

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

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Q: 2.) Find 1st derivative of y = e-'In (x-1)

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Q: f (x) = ln(x · 5*)

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

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Q: Determine the first derivative of the ff. function y = 2 + arctan(3 sec 2x)

A: We have to find the first derivative of the function: y=2+tan-13 sec 2x We know the formula of…

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

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Q: How do I use the method of logarithmic differentiation to compute dy/dx?

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Q: tan s) Differentiate f(x) = 5* log3 %3D csc 2x

A: Consider the function fx=5xlog3tan-1xcsc2x Here, the objective is to differentiate the function.

Q: What is the derivative of ln(sin x + cos x)

A: Consider the given function:

Q: State the derivative rule for the logarithmic function ƒ(x) = logb x.How does it differ from the…

A: Given: fx=logbx for finding derivative of given function, first we convert it's base in e then…

Q: Log Activity CALL l.y=log4 (3x2 -5x) In 9x4 2.y= 3.y= Inx3 X-5

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Q: What are the formulas for differentiation and integration? How are they applied?

A: To write: Formulas for differentiation and integration.

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: Find the first derivative of = (ln x)* 4 y

A: From the given function; y=lnx4 We know that; The Power law: ddxxn=nxn-1 The chain rule:…

Q: Find the derivative of n^(ln⁡(cosu)). Where n=822

A: Given information : nlncosu Here, n=822. we have to find the derivative of given function.

Q: What is the first derivative of the expression (xy)× = e?

A: See the details solution in below

Q: Find the derivative OF the exponential funchion y = In ( 5- e **) Please simplify it Further.

A: Consider the provided equation, y=ln5-e4x Find the derivative of the equation. Apply the chain rule…

Q: x(2x+3) 17. f(x) =- (x° +1)

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

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Q: What is the derivative of: y = ln ln(1 − cos x)

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

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

A: To solve the following problem

Q: Determine the derivative: y = log (3x2) (01)प य log (3) ** In(10) 6 log (Sx) r In(10) Oy= 18x In(10)…

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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 equation of the tangent line to the graph of f(x) = 4^(x/ln2) at the point where x is ln16.

A: We find dy/dx to find the slope at x.

Q: 6. y = (x² – 1)tnx

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Q: What is the derivative of the function  x^8(ln(x)), and what can I substitute for x to make the…

A: We have to find derivative dy/dx and point where dy/dx =0y is given below:

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

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

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Q: Find the second derivative of 2x^2 ln (1/x^2)

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Q: Compute the derivative ln(ex+1) / 2x+1

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Q: What is the first derivative of g(x) = ln #*+1? x2

A: Derivative of ln(x):       ddx(ln(x))=1x Division rule of derivative:-…

Q: 4. y=ln(4x' +5)

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Q: is the derivative of In

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Q: 2) Use logarithmic differentiation to find the derivative (Vx + 3)(x – 7)5 f(x) : (x3 – 4) - -

A: Given function is fx=x+3x-75x3-4 Given function can be re-written as: y=x+3x-75x3-4 Taking logarithm…

Q: What is the derivative of the function  x^8(ln(x))?

A: To find the derivative of the function x8(ln(x)) as follows.Redefine the function as follows.

Q: Find the derivative of the logarithmic functions: y = ln ( 4x^3 - x^2 + 1^2)

A: Application of derivatives

Q: Show that the derivative of f(x) =xln(x)−x is ln(x). Use this to compute∫ln(x)dx.

A: Sum/difference rule of differentiation,

Q: What is the difference between a derivative and an integration?

A: We have to state the difference between a derivative and integral.

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