Solve xdy = y(1+ ln y - In x)

Q: A sample population of strands of the bacteria is increasing at rate proportional to the population.…

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

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

Q: By using the definition of hyperbolic functions as exponential functions, show that sinh 3x = 3 sinh…

A: handwriting solution

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

A: Topic - derivatives

Q: Differentiate y = /sin(x² + 3)cosx

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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: Use linear approximation to estimate ln(.99)

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Q: A breeder reactor converts relatively stable uranium 238 into the isotope plu- tonium 239. After 15…

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Q: The half-life of radioactive cobalt is 5.27 years. Suppose that a nuclear accident has left the…

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Q: Differentiate  y=sin(ln(5x2-2x))

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Q: Differentiate y =( logx) sinx

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Q: 14. √ √2-√x dx

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Q: Differentiate with respect to the independent variable: y=tan[ln(3x2+5)]

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Q: find the second derivative of y=ln(e^x+e^-x)

A: Given query is to find the second derivative of the expression.

Q: A culture of the bacterium Salmonella enteritidis initially contains 50 cells. When introduced into…

A: Given: Initial population = 50. After 1.5 hours, the population size = 775. Given that the bacteria…

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: V3x+1(4x+1) (1– 2x)* Calculate y: y=

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Q: find an equation of the tangent line at the point indicated. y = log2(1 + 4x−1), x = 4

A: We have to find an equation of the tangent line at the point indicated. the given function is…

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

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

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Q: A storage battery discharge at a rate which is proportional to the charge. If the charge is reduced…

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Q: A storage battery discharge at a rate which is proportional to the charge. If the charger is reduced…

A: Solve by making equation

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: 2. y = [log(arccotx³)]coshx. Find dy/dx

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Q: Differentiate  y = ln(2x + 1)

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Q: A radioactive substance decays at a rate proportional to the amount present. If the initial mass of…

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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: The Smith's invest $10,000 in an account that grows to $12,000 in 5 years. What is the annual…

A: Consider the given smith invest $10,000 in an account that grows to $12000 in 5 years

Q: Investigate the root of the equation x+Ln x-5 = 0 in the range [3.2,4] using the Regula-Falsi…

A: Consider the given equation whose root is required to calculate.

Q: •2 5. Calculate | x In(3x)dx.

A: Given integral:

Q: The amount of radio active material present at time t is given by A=Aoe*t, where Ao is the initial…

A: As many Questions are given , I will solve only one: Let A0 be the initial amount. Given that a…

Q: How is ln x affected if x is multiplied by et?

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Q: 6. y = (x² – 1)tnx

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Q: A radioactive element is known to decay at a rate proportional to its present mass. Initially, there…

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: A quantity with an initial value of 310 grows continuously at a rate of 8.5% per second. What is the…

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Q: 22

A: Given,

Q: A breeder reactor converts relatively stable Uranium 238 into the isotope Plutonium 239. After 15…

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Q: for dx

A: Given integration is : ∫exdx To find the value given integration by parts.

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

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Q: |The amount A(t) of atmospheric pollutants in a certain mountain valley grows naturally and is…

A: Write the naturally growing equation as exponential function A(t). At t = 0, let A (t) be Ao and at…

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

A: Application of derivatives

Q: (a) Sizl=1 dz.

A: Here we use property of analytic function.

Q: Find dz using logarithmic differentiation if y (2z). %3D

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Q: 11) Find the first derivative of y = (ln x)*

A: We have to find the first derivative of given function.

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: Suppose a pollutant is seeping into the ground near a dump site at the rate of 2800 f(t) : (æ +…

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