Find the linearization of ƒ(x) = log3 x at x = 3. Then round its coefficients to two decimal places.

Q: find the n-th derivative of f(x). f(x)=e^-2x

A: Given function is fx=e-2x. Chain rule of differentiation states that: ddxfgx=f'gxg'x Now, we find…

Q: find f'(x) of (((3x^2+1)e^x^2)/(2x+1)^5)^5 using logaithmic differentiation.

A: The given function is,

Q: Find the derivative of the function. 2 a) f(x) = x² ln(x) b) g(x) = 2" + log, (x + 5) +ez c) y =…

A: We have to find the derivative.

Q: At what time does f (t) attain its largest value?

A: Consider f(t) is any function. We know that function attains its largest or smallest value when the…

Q: Find the derivative of the function.

A: We know that, logbx=y if and only if, x=by. Also, logbxn=nlogx

Q: Find the derivative of the function h(x) = log5 (x/x − 1)

A:

Q: Find the derivative of the function. y = In(e7x + 5)

A: Given y=ln(e7x+5)

Q: Find the equation of the line tangent to the graph of y=log, (5x + 1) at x= 2

A:

Q: Find the derivative of the function. y = log, v9x + 1

A:

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

A:

Q: Q1: Find the derivative of the functions. 5- y = (csche)(1- In csche) 6- y = log3 (1 + 0 In 3) %3D

A: 5. y=cschθ1-ln cschθ6. y=log31+θ ln3

Q: Find the derivative of the function. y = log 4 V3x +2

A: The Answer is Option A

Q: Find the linearizationsof the following functions at x = 0. ex

A: fx=ex at x=0. Now differentiating with respect to x, we get f/x=dexdx=ex Now, f0=e0=1 & f/0=e0=1

Q: sketch the shifted exponential curves y = 1 - ex and y = 1 - e-x

A: Given  The parent exponential function y=1-ex . To find the graph of the exponential function…

Q: 5. Use the chain rule to find the derivatives of (a) y = log; V4 + 1 (b) y = (x – e-")²

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Q: S-2(x-1 - x²) dx 5.

A:

Q: compute a formula for the nth derivative of f(x)=e2x

A: We have givenWe have to find a formula for nth derivative of f(x)

Q: Find an equation of the tangent line to the graph of the function  y = log3 x, at the given point…

A: y = log3 x

Q: Find the derivative of the function y = In(8 – e-a f'(x) =

A: We have to find derivative

Q: Find the derivative of the function f(x) = log23√(2x + 1)

A: To find derivative of fx=log22x+13

Q: Determine the equation of the tangent line to the graph of y = f'(x) at the point where x = 1 if…

A:

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: Find the linearization of the function f(x)=ln(2x+3) at x=-1

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Q: Find the derivative of the function. y= log , (3x2 - 2x) 5/2 O A. In 9(3x- 1) (3x2 - 2х) OB. 10(3x –…

A: We need to apply 1.chain rule 2.differentiation of logarithmic   we get option c as correct answer

Q: Exercise 9. Use properties of logarithms to find the derivative of S(2) = In (3z – 2)(v/=" + 1))…

A: From the given problem;   fx=ln3x-2x3+1   From the property of the log.   lna·b=lna+lnb   So, we can…

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 derivatives of the functions y = log2 (x2/2)

A: Given that y=log2(x22)

Q: Find the derivative of the function y = log5 √(x2 − 1 )

A: Here given function as y=log5x2-1 or y=log x2-1log 5 The power rule for derivatives is expressed as…

Q: find the second derivative of y = x In x A 1/x в) 1/2х D) 2x

A:

Q: Suppose that the DE dy = y(90 – y) – 2000 dt models a logistic equation with harvesting, where y(t)…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

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

A:

Q: Find the slope of the tangent line to the exponential function at the point (0, 1). y 2 1 (0, 1) -2…

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Q: Q3: find the derivative of In(x4+3x-1) a) f(x) = %3D x²+1 b) f(x) = 4x³ . log(x² + 2x) %3D c) f(x) =…

A: Use product rule of differentiation.

Q: y = log4 x %3D .y = In(5x2 -4x + 8) %3D

A:

Q: Find the derivative of Log(z²). 2/22 1/22 1/z 2/z

A: The correct option is 4th option.i.e. 2z .

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: Find the derivative of the function. y = log 6 V3x+7 3. O A. In 6 3 In 6 O B. 3x +7 In 6 (3x + 7) 3…

A: Given, y = log63x + 7Applying the log rule; logab = lnblnay = ln3x + 7ln6Differentiating with…

Q: Compute the derivative of the given function. log3 x f (x) = %3D cot x - 2x2

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Q: Find the derivative of the function

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

Q: Solve for the derivative of the following Exponential Differentiation. 1. y = 92x^2 + 3x +1 2. y =…

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Q: Find the anti-derivative of g'(x)= log1/2(X)

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Q: Find the PV of an income stream that pays out continuously at a rate R(t) = $5000e0.1t /year for 7…

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Q: Find the derivative of the function. g(x) = [*- 1 -dt -5 2+4 10 а. 841 b. 2x (x²+ 4)² 1 С. x²+4

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Q: Find each derivative 1)f(x) = e*+&r+1 2) g(1) = In(?* – \H x*(x7–3)² . 3) y = In(2 Vx+10 ) [Hint…

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

A: