Find the second derivative of the f(x)=9+8x ln x function

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 log functions: y = ln(x√x2 – 6) f(x) = ln(2x/x+1)

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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: Find the first derivative of g(x) = - 9e* tan(x). : (x),6

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Q: Find the second derivative of the function.         f(x) = csc x

A: Differentiating with respect to x, we get

Q: Find the derivative of the logarithmic function. f(x) = 2x² In 2x f'(x)= 2n +4n in (2n) X

A: Follow the procedure given below.

Q: compute the derivative f (x) = ln(4x2 + 1)

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Q: Determine the first derivative of the ff. function y = ln| le* – 1/

A: We have to find the first derivative of the function: y=lnexex-1 We know the property of logarithm,…

Q: Find the first derivative (x^5+6x^3+10x)/√x

A: To find: The first derivative of . Formula used: Quotient rule of derivative: Power rule of…

Q: Find the second derivative of f(x) = (5+7x)e5". f" (x)

A: Topic :- Differentiation

Q: Find the second derivative of the function. 3root(x) + e^(6x)ln(x)

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Q: Find the derivative of f (x) = 9ª ln (x).

A: Given: f(x)=9xln(x)

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

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

Q: Find the derivative: y = 6 In x 6 ln x-1 x7 1-6 ln x 12 1+6 ln x x12 4 O 1-6 ln x x7 O

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Q: Determine whether the following statement is true or false, and explain why. The derivative of ln kx…

A: if y = ln x Then y'=1x

Q: Find the second derivative of the function. f(x) = e-x3/3

A: Given:fx=e-x33Differentiation formula:ddxex=ex.1

Q: find the first and second derivatives of f(x) = ln (x+1)

A: f'(x)=1x+1 and  f''(x)=-1(x+1)2

Q: find the derivative of ln(3x^2+e^x)

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Q: FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM 3. y = ln (x3(x-1)/(x-2)2)

A: using the properties of log lnmn=lnm-lnnlnmn=lnn+lnmlnmn=nlnm As per our guidelines we are supposed…

Q: Find the derivative of f (x) = ln| x3 - 10x2 + 8| .

A: Given        f(x)=lnx3-10x2+8

Q: Find the derivative of the function. f(x) = 2x2 In 2x f (x)= 2x[1+2 log(2x)]

A: fx=2x2ln2x

Q: Find the fourth derivative of f(x)=7x+ln(x)-188x

A: ddx(ax) =axlogaddxlnx =1xddxxn=nxn-1 ddxc = 0 c is constant

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 = ln 4x / (x − 6)

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Q: 17. f(x) x²(2x+3) (x² +1)*

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Q: • Use logarithmic differentiation to find the derivative of y = f(x) = 1-x)²V4+x² (3x-5)* • Find the…

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Q: x(2x+3) 17. f(x) =- (x° +1)

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Q: Find the second derivative of the function. g(x) = √x + ex ln x

A: Consider the given function gx=x+ex lnx Now, differentiate the given function with respect to x…

Q: Find the derivative of g(x) = ln(2x + 5)

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Q: - - Find the fourth derivative of f(x) = 5 + ln (x) — 127.

A: Topic = Derivative

Q: Find the second derivative of the function. In(x) f(x) = + 6x? -4x° – 18xln(x) + 3-6 ln(x) + 12…

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Q: Find the first derivative of f(x) =x3/e3x

A: Given : fx = x3e3x

Q: 10) Find the second derivative of f(x) = 3e³x − 8e-6x 5x

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

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Q: Find the derivative of the function. f(x) = ln(8x + 9)

A: Given, f(x) = ln(8x + 9)  We have to find the derivative of the function.

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 derivative of: h(x) = ln(2sec(x))

A: topic - derivative of a function  derivative of: h(x) = ln(2sec(x)) is tan x

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

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

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Q: Find the derivative of the logarithmic function. f(x) = 2x² In 2x f'(x)= 4in (2x) + 6

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

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

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Q: Find the derivative of the function   f(x)=ln(x3(2x+1)/x^2−3)

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Q: Find the first derivative of:   f(x) = ln [(5x+2)1/2 / csc(x)]

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

A: Application of derivatives

Q: 7. y= ln 2x³ 5х-3

A: Explanation of the answer is as follows

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: Find the derivative of the function y = 1/ln(1 − 7x)

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Q: Find the derivative of f(x)= ln x^2/x^2+1

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Q: Find the fourth derivative of  f(x)=7x+ln(x)−125x.

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Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in terms of global or local range. The definition of minimization in the thesaurus is the process of reducing something to a small amount, value, or position. Minimization (noun) is an instance of belittling or disparagement.

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which one would be easier? Walking on the road would be much easier than climbing a mountain.  

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the first derivative test and second derivative test to understand the concave behavior of the function.