Differentiate   y = ln(x2 + 1)/(x2 + 1)

Q: find y' for y = 2Vsinx sinh-1(logx). %3D

A: y'=log2· 2sinx-1.cosx.sinh-1(logx)sinx+2sinxxlog2x+1

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

A: Topic - derivatives

Q: Integrate 01-In x + C о √(5-2) x – 10 ln |x| X - - - 1 10 In |x| 2 25 Olnx-25x + C ▬▬▬▬▬▬▬▬ X dx. +C…

A: Topic = Integration

Q: Differentiate  y=sin(ln(5x2-2x))

A:

Q: Differentiate  f (x) = 1/ln(x4 + 5)

A: We have the given function as fx=1lnx4+5         ⋯⋯1 We know that, from the quotient rule of…

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: use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos4…

A: Given: y=cos4θ

Q: What is the derivative of the natural logarithm function ln x? How does the domain of the derivative…

A: Given: fx=ln x To find: (a) The derivative of f(x)  (b) Compare the domain of the derivative with…

Q: Evaluate the derivative: y = log2(log2x)

A: It is given that,

Q: Find the first derivative:  y=log1o 5x+3/5x-4

A:

Q: What is the first derivative of s(x)=(6x)^3x at x=3? Enter an exact answer in terms of a natural…

A: We will take the logarithm with base e and then find the derivative with respect to x and then…

Q: find derivative d/dx ln(3x/(2x+7)^1/2)

A:

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

A:

Q: 5) Find the derivative using logarithmic differentiation: y = Xcanx

A: As per our guidelines we are suppose to solve only first question. Kindly repost the other question…

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

A:

Q: Use logarithmic differentiation to evaluate y'. y = (8x)ln8x

A: Differentiation: - Differentiation is the ratio of a slight change in one quantity to a little…

Q: Find the antiderivative of antiderivative of x2(ln(10x))2

A:

Q: Find the derivative: ln ((x+1)/(2x-1))^(2)

A: First simplify the expression using properties of lograthim than take derivative.

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: Suppose that $15,000 is invested and at the end of 3 yr, the value of the account is $19,356.92. Use…

A: Given :            $15,000 is invested and at the end of 3 yr, the value of the account is…

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

A:

Q: Differentiate  y = ln(2x + 1)

A:

Q: Differentiate  y = ln(4x2 - 2x + 9)

A: To differentiate  y=ln(4x2-2x+9) The given function is a composite function, Hence, let u=4x2-2x+9…

Q: Integrate ∫(ln(x))/x

A: We need to integrate the given logarithm function:

Q: Use the General Power Rule, Exponential Rule, or the Chain Rule to compute the derivative. y = cos4…

A: Using chain rule to compute the derivative for y, consider the solution below.   First of all,…

Q: What's the derivative of ln(ln(ln(lnx^3)))

A:

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

A:

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

A:

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: fx=lnx,  gx=ln2x

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

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

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

A:

Q: What is the derivative of (ln(3x))/x^6?

A: Let y = (ln(3x))/x6.The derivative of y is with respect to x as follows.

Q: Compute the derivative of (ln x)^ln x

A: To find the derivative of (ln x)ln x Using the exponent rule ab=eb ln a we get, (ln x)ln x=e(ln x)ln…

Q: Differentiate the function. y=ln(x5sin2x)

A: Given function:

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

A:

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

A:

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

A:

Q: Calculate the derivative. y=3/log5x

A: Given function is

Q: Find the derivative of f(x) Give answer in exponential notation with positive exponents

A:

Q: find the equation of the tangent line to the graph of the logarithmic function at the point (1,0)…

A: Given problem:- find the equation of the tangent line to the graph of the logarithmic function at…

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A:

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

A: Application of derivatives

Q: Find the derivatives of x log x.log(logx)

A: We have to find the derivative of-  x logx.log(logx)

Q: What is the derivative of log (x²)? ○ 2x-log(x²) 1 x² 2x O log(2x) O exp(2x)

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

A: Given, d2dx24 log2x-5

Q: derivative of log,10x is :

A: