Find the derivative of the functions below: In(x) (a) g(x) = log,(x) g'(x) = (b). y- in(6x®)

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y= ln x3

A: Given:

Q: Find the derivative of the logarithmic functions: y = ln (tan^2 θ )

A:

Q: Find the second derivative for the functions defined as follows g(x) = 4x(ln x)

A: We have to find second derivative of the function: gx=4x lnx Since two function are in product so we…

Q: Find the derivative of the function. f(x) = ln 3x

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Q: Find the derivative of f(x)=ln(x^3-x+2)

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Q: Find the derivative using the logarithmic y=ln (x+1)/x^2-2

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Q: L(x) = In(x)+log,(x)

A: Used formulas : ddx(logax) = 1x ln a ln x = loge xloge e = ln e = 1ln 5 =1.61

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

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Q: find the derivative of the function  y'=ln(squared root of x^2-4) and  y=ln IsinxI

A: The given function is y=lnx2-4. Obtain the derivative as follows.…

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

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Q: Find the derivative of y =log2x

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Q: Find the derivative of the functions. y=cosh^-1 (3x)

A: We have to find derivative of the function: y=cosh-13x Rewriting the function, y=cosh-13xcosh y=3x…

Q: Find an expression for the derivative of the exponential function y=ex using the definition of…

A: To determine the derivative of exponential function y=ex using definition of derivative.

Q: Find the derivative of ln(2x2)+ln(2x)+1/3 where x=1

A: Given,           The derivative of  ln2x2+ln2x+13 where x=1

Q: Find the derivative of y=sinh-17x

A: Given:y=sinh-17xHyperbolic Identity:cosh2x-sinh2x=1Differntiation formula:ddxsinx=cosx

Q: Find the derivative of the function f(x) = 5ª+x² + log3 (In x). %3D

A: To find the derivative of the given function.

Q: Find the first derivative y= etanx

A: We have to find first derivative of    y=etanx   First derivative is dydx

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 the function. y = In(x?)

A:

Q: Find the derivative of the function. y = ln∣csc x∣

A: Given data:   The given expression of the given function is: .   Substitute u for csc x in the given…

Q: x(2x+3) 17. f(x) =- (x° +1)

A:

Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

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Q: Find the derivative of y = etanx

A:

Q: Find the derivative of the function. f(x) = ln 2x/(x + 3)

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Q: Find the derivative of the function h(x) = x2 arctan5x

A: The given function is h(x) = x2 arctan5x

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = 1/ln 3x

A: Given:

Q: Find the derivative of y with respect to the appropriate variable. y = cosh12 x+ 5

A:

Q: Find the derivative of the function

A: We have to find the derivatives of the function: y=x tan-12x-14ln1+4x2 If two functions are in…

Q: find the derivative of y with respect to the givenindependent variable. y = log4 x + log4 x2

A: Given: By using logarithm base change rule, the function can be rewritten as follows,

Q: Find the derivative of the function y, below. 9x(ln x + In 2) – 8x + v2 %3D

A: first, simplify the function  y=9xlnx+ln2-8x+2 y=9xlnx·2-8x+2 y=9xln2x-8x+2

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: Find the derivative of the function.   y = In(x)/x9

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

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Q: 19. Find the derivative of 16 = xy using implicit differentiation.

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Q: Find the derivative of ƒ(z) = ln2x 1. 2z

A: We first expand using the addition property of log.

Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

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Q: f y = (sin x)x b

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Q: Find the derivative of y= log, (5x³)+log, (sin.x)

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Q: Use Delta method to find the derivative of e*

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Q: Shows the derivative function of: x³  + ln x(3x² + 5)

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Q: 4.x³ (log3 x)° b. y = (csc5 x) /sinh(2x – 8)

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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 y with respect to x, t, or θ, as appropriate. y = ln (ln x)

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Q: find the derivative of y with respect to the givenindependent variable. y = log5 ex

A: On simplification, we get

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

A: Application of derivatives

Q: use logarithmic differentiation or the method to find the derivative of y with respect to the given…

A:

Q: find the derivative of y with respect to x, t, or θ, as appropriate. y = ln 3x + x

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Q: Find the derivative of y = arccos x + x 1-x²

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Q: Find the derivative of the function y = ln 5x/(1 − x)

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