Given that f(x) = 3^x and g(x) = ln(x), evaluate both (g ◦f)(2) and (f ◦g)(2). If necessary, round your final answer to three decimal places. Do not round more than necessary in any intermediate steps.

Q: Find the derivative using the logarithmic y=ln (x+1)/x^2-2

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Q: Find the derivative of f( x ) = 2° log3(z + 2.5) f'(x) =

A: The first derivative of the function is . The product rule of the differentiation is .

Q: Find the First Derivative: y=log10(5x+3/5x-4)

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Q: find the derivative using logarithm of y= (x+2)^2

A: Take ln on both sides Then differentiate both sides with respect to x

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

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Q: y = log v2x + 5

A: i have provided this answer with full description in step-2.

Q: Without using a graphing calculator, how can I show the function 1-ln(y )= z in a graph and its…

A: Without using a graphing calculator,  Show the function zx,y=1-lny in the graph and its traces.

Q: Evaluate the limit or derivative using properties of logarithms where x3 needed. dx x5+1

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Q: Find the first derivative:  y=log1o 5x+3/5x-4

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Q: x+1

A: By using the formula you can solve the given problem as follows :

Q: What is the first derivative of s(x)=(6x)^3x at x=3? Enter an exact answer in terms of a natural…

A: We will take the logarithm with base e and then find the derivative with respect to x and then…

Q: 5th derivative of y = log x^5 to the base 2

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Q: Find the derivative of y =log2x

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Q: Find an expression for the derivative of the exponential function y=ex using the definition of…

A: To determine the derivative of exponential function y=ex using definition of derivative.

Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: If f(x) and g(x) is any function then, If limx→∞f(x)g(x)=∞ then f(x) grows faster than g(x). If…

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

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

A: We need to differentiate the following function.   y = ln(3x+1) - ln 3

Q: State the derivative rule for the logarithmic function ƒ(x) = logb x.How does it differ from the…

A: Given: fx=logbx for finding derivative of given function, first we convert it's base in e then…

Q: Log Activity CALL l.y=log4 (3x2 -5x) In 9x4 2.y= 3.y= Inx3 X-5

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Q: Evaluate the derivative. * d (log10 (x)) dx (In(10)) O Option 1

A: we have to find the derivative

Q: What are the domain and range of ln x?

A: Given: y=lnx we know that in lnx, x>0 so, domain of given function is x>0

Q: What is the first derivative of q(x)=(3x)7x at x=2?  Enter an exact answer in terms of a natural…

A: When there is variables in exponent we should take log both side then differentiate. Here we use…

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

A: fx=2x2ln2x

Q: Derermine The FirST derivative of : 千irsT OF F) = x³ .16 V5メ-2 こSioN Expa usiNG Logalith mic Ex…

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Q: Find where the first derivative is equal to 0. Er ****. lif

A: Introduction: The concept of critical point is very important in Calculus as it is used widely in…

Q: 2. y=cot1-2x 3. y=log22x*

A:

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: Calculate the derivative and use logarithm rules to simplify   g(x) = ln((x^3 + 2x)(x+1)^10)

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Q: Determine the derivative: y = log (3x2) (01)प य log (3) ** In(10) 6 log (Sx) r In(10) Oy= 18x In(10)…

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Q: Use limit methods to determine which of the two given functions grows faster, or state that they…

A: fx=x2lnx gx=ln2x⇒gx=lnx2 limx→∞fxgx=limx→∞x2lnxlnx2limx→∞fxgx=limx→∞x2lnx

Q: Find an equation of the tangent line to the graph of the logarithmic function at the point (1, 0). y…

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Q: Find a number such that the tangent line to the graph y= log,(x) at x = a is parallel to the tangent…

A: The objective is to find the value of a

Q: Find the derivative   Y=ln(4+X^2 )

A: The given function is,

Q: What is the derivative of: log x/(x+1)

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

A: Tangent to a curve is a line which just touches the curve and in some sense is parallel to the…

Q: find the derivative of y with respect to the givenindependent variable. y = log2 (8tln 2)

A: We first expand the equation using the addition property of log and the change of base property.

Q: Find the nth order derivative of the natural logarithm function y=lnx.

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Q: Find the derivative of the natural logarithm y=lnx.

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Q: In the scenario of the derivative of a logarithmic function, determine the slope of the tangent line…

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Q: ミr

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Q: Find the derivative of f(x) Give answer in exponential notation with positive exponents

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Q: find the equation of the tangent line to the graph of the logarithmic function at the point (1,0)…

A: Given problem:- find the equation of the tangent line to the graph of the logarithmic function at…

Q: 2) Use logarithmic differentiation to find the derivative (Vx + 3)(x – 7)5 f(x) : (x3 – 4) - -

A: Given function is fx=x+3x-75x3-4 Given function can be re-written as: y=x+3x-75x3-4 Taking logarithm…

Q: 2x+3) 17. f(x) =- (x² +1)*

A: topic - logarithmic differentiation

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

A: Application of derivatives

Q: Find the derivatives of x log x.log(logx)

A: We have to find the derivative of-  x logx.log(logx)

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: what is the Derivative of Exponential Functions?

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

A: Given, d2dx24 log2x-5

Q: Find the equation of the tangent line to the curve y = log(x2-3x+1) at the point (3,0)

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: