Integrate ∫(ln(x))/x

Q: y = (In x)* xln x

A: Explanation of the answer is as follows

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: Differentiate y = /sin(x² + 3)cosx

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Q: Use logarithmic differentiation or an alternative method to find the derivative of the function. y =…

A: Given that  y=(sin9x)^(lnx) To find the derivative of y

Q: 15.) X (2x+5) 2 dx

A: Indefinite integral

Q: Differentiate  y=sin(ln(5x2-2x))

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Q: Differentiate y =( logx) sinx

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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: (A) Ln(2) S Sinh(x) Cosh² (x) dx

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

A: It is given that,

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

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Q: Find the indicated derivative and simplify. [6x log x°] dx [6x log x ]= 125 dx (Type an exact…

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Q: Use logarithmic differentiation to find dy/dx of y=(lnx)lnx

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

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Q: Find the derivative of the logarithmic function. 6 + y = In

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Q: Find the derivative: y = x [ln(x) - 1] O ln(x) - 1 о O x ln(x) O In(x) O 1 + In(x)

A: Given y=x[lnx-1]To find dydx:

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

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Q: 1. ļ | sinh 3x dx

A: The objective is to evaluate the integrarion.

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: Find the slope of the tangent line to the exponential function at the point  (0, 1). y = ex/3

A: Slope of tangent line is derivative of the given function at that point.

Q: Find ∫cosh 2x sinh2 2x dx.

A: To find the value of the integral∫cosh2xsinh22xdx

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: 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: Calculate the derivative and use logarithm rules to simplify   g(x) = ln((x^3 + 2x)(x+1)^10)

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Q: Verify the formulas by differentiation. ∫ 1/x + 1 dx = ln | x + 1 | + C, x ≠ -1

A: We have to verify by formulas of differentiation where expression is given as: ∫1x+1dx=lnx+1+C, x≠-1…

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: Use log differentiation. y = (cosx)lnx

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

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

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

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

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

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Q: tanh 2x In (cosh 2x)dx

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Q: Integrate f sinh 2x dx

A: In this question we have to find Integration.

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

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

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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: Use logarithmic differentiation or an alternativemethod to find the derivative of the function  y =…

A: Given:y=sinxlnx

Q: 3 sin-xe 5%

A:

Q: Apply logarithmic differentiation given the ff: In x

A: y=xln xtaking ln on both sides ln y=ln xln xlny=ln(x)*ln(x)         ln xa=alnxln y=(ln(x))2…

Q: Use logarithmic differentiation to find the derivative of y with respect to the independent…

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

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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: what is the Derivative of Exponential Functions?

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

A: Given, d2dx24 log2x-5

Q: derivative of log,10x is :

A: