If f(x) = 4x² ln(7x), then %3D f'(x) = f" (x) = f" (x) =

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: It is estimated that t months from now, the population of a certain town will be changing at the…

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Q: The amount of plutonium remaining from 1 kilogram after x years is given by the function…

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Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: given,     radioactive material is decay at a rate proportional to the amount present .initially 50…

Q: Find the first derivative of the following functions Y = x5 e-3 ln x and Y = ln √ [ (x – 1 ) / ( x…

A: Solution is given below:

Q: 5. Find the instantaneous rate of change of 1 g(x) = 2x – 32x° + 17x² – 9x + 4 at x = 2

A: Given equation is, gx=2x4-32x3+17x2-9x+4

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

A: Given the  y = ( ln x)^4 We need to find the first derivative . Therefore differentiate to given…

Q: 2. The rate of decay of radium is proportional to the amount present at any time. If 60 mg of radium…

A: A(t) = amount remaining in t years          = A0ekt, where A0 is the initial amount and k is a…

Q: Locate the relative extrema of y = ln(x2 + 2x + 3).

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Q: Solve for x accurate to three decimal places ln x + ln(x − 3) = 0

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Q: The population of a certain municipality increases at the rate proportional to the present…

A: Here we solve the given population growth problem.

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

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

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Q: Find the anti-derivative of: S(3x* – 6x)° (2x³ – 1)dx

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Q: s projected that x years from now the population of a certain city will be changing at the rate of…

A:

Q: If the total revenue function for a blender is R(x) = 41x – 0.01x² where x is the number of units…

A: Given that, the revenue R (in dollars) for a blender is given by  R(x) = 41x - 0.01x2 where x is the…

Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

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Q: A certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: Let us assume that the rate of change of the amount of material is proportional to the amount of…

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

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Q: Find the given derivative 6 Dx 7x 1 Dx 7x 5 LN +

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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 the function y = ln 4x / (x − 6)

A:

Q: certain radioactive material is known to decay at a rate proportional to the amount present. If…

A: We will solve the radioactive decay problem.

Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

A: The amount remaining after hours 24 hours is 88.5 milligrams.

Q: Integrate ∫(ln(x))/x

A: We need to integrate the given logarithm function:

Q: A certain population of bacteria doubled after 20 minutes. If it is known that it grows proportional…

A:

Q: If the total revenue function for a blender is R(x) = 28x – 0.01x² where x is the number of units…

A: To find The average rate of change of revenue R(x) as x increases from 10 to 20 units.

Q: Find the derivative   Y=ln(4+X^2 )

A: The given function is,

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: 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: solve the first and second derivative of Y= (1+lnx)  /  x

A: If y=f(x), then the independent variable x is called the input of the function, and the dependent…

Q: If the area A = s of an expanding square is increasing at the constant rate of 8 square inches

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

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Q: Find the equation of the line tangent to the graph of y=(x^2−x)ln(7x) at x=2. Round to three…

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Q: Find the differential of the function y=lntan2x at x=π/8.

A: Given: ,at x=π/8 Differentials are infinitely small quantities. Use the term for differentials as…

Q: Initially 100 millions of radioactive substance was present. After 6 hours the mass has decreased by…

A: Given query is to find the amount of radioactive substance after 24 hours.

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

A:

Q: Find the instantaneous rate of change of g(x)=(x^3-sqrt(x))e^x+(x^5-2x+3)ln(x) when x=3. Round to…

A: The instantaneous rate of change of g(x) is:…

Q: Calculate the derivative of the function y=log2 x ln (2x) at x=1.

A:

Q: A bacterial population Y is known to have a rate of growth proportional to Y itself. If between noon…

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Q: It is projected that x years from now the population of a certain city will be changing at the rate…

A:

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

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Q: If the rate of change of y with respect to x is equals to 2-y and y=8 and x=0. Find y when x=ln(2).

A: Given: The rate of change of y with respect to x  is equal to 2-y. That is, dydx=2-y

Q: The half-life of plutonium 239 is 24,200 years. Assume that the decay rate is proportional to the…

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

A: Given, d2dx24 log2x-5

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

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Q: Find the derivative.  y = ln((x + 1)(2x + 9))

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: