Which of the following functions grow faster than x2 as x→∞?Which grow at the same rate as x2? Which grow slower? x ln x

Q: Differentiate the following function.   y =ln (x2 + 1) / (2x + 3)

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Q: 9)/6)= (2x+1)*

A: As per our guidelines we are suppose to solve only first question if the multiple questions are…

Q: Which of the following functions grow faster than ex as x→ ∞?Which grow at the same rate as ex?…

A: We find the limit of the ratio of the two functions

Q: Differentiate the following function.   y = ex ln x

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Q: Differentiate the following function.   y = ln(x2 + ex)

A: Given function is y=lnx2+ex. To differentiate the function. Solution: Power rule of differentiation…

Q: Which of the following functions grow faster than In x as x→ oo? Which grow at the same rate as In…

A: fx=lnx c. gx=1x Now, limx→∞gxfx=limx→∞1xlnx=limx→∞1x lnx=0 Hence fx=lnx and gx=1x grows at same…

Q: Differentiate the following function.   y = ln(9x)

A: Consider the following function:      y=ln(9x) Find the derivative of the tunction.

Q: Find the derivative of the function F(s) = In(9 ln(8s)). F'(s)

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Q: - Which of the following functions grow faster than In x as x→ o0o? Which grow at the same rate as…

A: Derivative of a function determines the change of variable with respect to another variable. Whereas…

Q: Suppose that f(x) = 11x – 4 ln(x), x > 0.

A: (g) Find the double derivative for f(x).…

Q: Differentiate the following function.   y =  ln -2x + 1

A: Given function is y=ln-2x+1. To differentiate the given function. Solution: Chain rule of…

Q: If f(x)=In(x-1), find the formula for f^((n))(x), the nth derivative of function f(x) f(x) = ln (x –…

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Q: What is the value of ln[f'(2)] if f(x) = e^x?

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Q: need fast

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Q: II. Determine the derivative of the ff. logarithmic functions 7. y = 12x² log 8x 8. y = In 25x %3D…

A: Solution is below

Q: Find the equation of the secant line for f(x) = log2 (3x² + 2x – 1) from x = 1 to x = 3.

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Q: Differentiate the following function.   y = ln (1/e1x)

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Q: Q2) find the derivative of the functions : 10 logą t (3x²-1 1) y 2) f(x) = 2x+5

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Q: Q2/ Find the derivative of each of the following functions:- X 2. log₂ x y = X 1+ tan x 1. y=(sin…

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Q: Differentiate the following function.   y = e2 ln(2x+1)

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Q: 4. Which of the following functions grows at the same rate as ex as x goes to infinity? ex+3 e3x e2x…

A: We find which of the following functions grow at the same rate as ex as x goes to infinity: (1) ex+3…

Q: Differentiate the following function.   y = ln(ex2/x)

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Q: A bacteria colony grows at a rate of 11% per year. If the initial sample has a mass of 500 grams,…

A: We are given that the grow after each year is 11%, that means if the initial value is x, then the…

Q: An environmentalist finds that a certain type of tree grows in such a way that its height h(t) after…

A: The rate at which the height of the tree changes is given by,h'(t)=3t2+t    ft/yr…

Q: The population of a colony of bacteria is modeled by the function P(x) = 50(e-X -e-X* ) + 10, for 0…

A: Given that: P(x)=50(e-x-e-x2)+10

Q: Determine the first derivative of the ff. function x? + 1) y = V1 + In x

A: y=x2+11+lnx

Q: Calculate the derivative of the following function. y = log 11(x-11) d. dx log 11(x- 11) =

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Q: Differentiate the following function.   y = ln(ex + 3e-x)

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Q: ) Find the first derivative: b) y = log7 v1+x

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Q: Find the first derivative. x= -6t + 4t+ 1 xp dt

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Q: Differentiate the following function.   y = ln(x6 + 3x4 + 1)

A: This question is taken from the derivative in which we have to find the derivative of the given…

Q: As x increases uniformly at the rate of 0.002 feet per second, at what rate is the expression (1 +…

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Q: y = log,(4x - 8x)

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Q: Which of the following functions grow faster than ex as x→ ∞?Which grow at the same rate as ex?…

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Q: 4 f (x) = 3 (In (9x² + 7(log5(+Vx*

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Q: Find the derivative of each of the following functions:-- log₂ x 2. y= X

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Q: Differentiate the following equation.  f(x)= (ln x)3 ex

A: Given:- f(x) = (ln(x))3 ex  To find :- Differentiate the given function f(x)

Q: Find the derivative of f(x) = In (x* V8 – 6x), using the properties of the logarithm. Provide your…

A: I have stated the used formulas in the solution

Q: Find the first derivative or f'(x) of the function below using the techniques of integration f (x) =…

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Q: Q3// By using logarithmic differentiation and with respect to independent variable x, find the…

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Q: Calculate the derivative of the following function. y=6 log 3 (x - 9) d 6 log 3 (x - 9) =D dx

A: d/dx [ f(x) ] = 1/ f(x) * d/dx[f(x)]

Q: Find the equation of the tangent line to the graph of f(x) at x = 2, if 25 f(x) = 2.5 + log5 2 (x -…

A: For x=2 f(x)=2·5x+log5252xf(2)=2·52+log5252(2)f(2)=2(25)+log525f(2)=50+2f(2)=52 So the point is…

Q: What is the derivative of the given logaithmic function y = log3 (2x“)? 2 In (3z) 2 A. æ In (3) 2 В.…

A: Let's find.

Q: Find the derivative of the function

A: given h(x)=log3xx-12we have to find the derivative of the given function

Q: Which of the following functions grow faster than ln x as x→∞?Which grow at the same rate as ln x?…

A: Let f(x)=5ln x       and g(x)=ln x,

Q: Which of the following functions grow faster than ex as x→ ∞?Which grow at the same rate as ex?…

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Q: Find the derivative of the exponential function f ( x ) = 5x 2 e 7x

A: Given function: f(x)=5 x2 e7x     Calculate the derivative of f(x): f(x)=5 x2 e7x   Take the…

Q: Find the derivative of the following: 8 f(x) = 3 (log5 ( – 2/x7 + x))* - e(v3³n²)

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.