Differentiate f (x) = loge (x26")

Q: Solve th equation for x. 22/log5x = 1/16

A: The logarithmic function is defined as the anti function of the exponential function. The…

Q: Is ln xy = ln x ln y a valid property of logarithms, where x > 0 and y > 0? Explain

A: ln(xy)=ln(x)+ln(y) using the addition property of logarithm. Where x>0 and y>0.

Q: State the Chain Rule version of the derivative of the natural logarithmic function in your own…

A: The derivative of the composite function is known as chain rule in calculus. Consider the natural…

Q: take natural log from both sides and solve the right side using the log rules. Then, take derivative…

A:

Q: Show that S log(sin x) dx = -log 2.

A: To show that ∫01logsinπxdx=-log2 using the given figure.

Q: Since the data obtained as a result of 5 observations of an experiment is ∑ log Xi = 6.27, what is…

A: n = 5 ∑ log Xi = 6.27 We have to find the geometric mean.

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

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Q: What is the derivative of the natural logarithm function ln x? How does the domain of the derivative…

A: Given: fx=ln x To find: (a) The derivative of f(x)  (b) Compare the domain of the derivative with…

Q: Evaluate the derivative: y = log2(log2x)

A: It is given that,

Q: x+1

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

Q: y = (cos(x²))* -2 Co:

A:

Q: Suppose that a population grows according to a logistic model with carrying capacity 6500 and k =…

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Q: Differentiate. y= 11* . log 7x dx (11*. log 7x) =O

A: Given that

Q: tan s) Differentiate f(x) = 5* log3 %3D csc 2x

A: Consider the function fx=5xlog3tan-1xcsc2x Here, the objective is to differentiate the function.

Q: 3 log25 x = 2

A: It is logarithms problem.

Q: Suppose the rate of net investment is given by I (t) = Lnt, find the total capital accumulation…

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

A:

Q: 2. Evaluate sin2x logtanx dx

A: Use the property of the definite integral and simply solve it.

Q: Find d/dx(2x) Type ln(x) for the natural logarithmic function.

A: Given query is to find the derivative of 2x.

Q: 2log x-1=log(x-1)

A: Given:  2logx -1=log(x-1)we know that alogb =logba   then 2logx=logx2Then    logx2-1=log(x-1)…

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

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Q: Find the derivative of the logarithmic function. 3x f(x) = In %3D x+2,

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Q: Use properties of logarithms to find the derivative of f(r) = In ((2. 2)

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Q: x(2x+3) 17. f(x) =- (x° +1)

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Q: Expand ln 3√y3z2/x4 as a sum, difference and/ or the consent multiple of logarithms.

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Q: Find all x- and y-intercepts of graph of y = -3 +log2(x2 - x +2).

A: Given function is y=-3+log2x2-x+2

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: 7. Use properties of logarithm to expand In (y³z²Vx – 1)

A: Property of logarithm

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

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Q: Differentiate with respect to the independent variable: f(x)= log base 20 square root x

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Q: Find the second derivative of 2x^2 ln (1/x^2)

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Q: Differentiate the following logarithmic functions and show that y=ln(x+5)2≠[ln(x+5)]2

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Q: How do I expand this logrithmic equation? In(x2 square root of y/z)

A: Given:

Q: (b) Show that 1 1+ 2 tanh- (2) = ; log

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

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Q: Calculate the derivative. y=3/log5x

A: Given function is

Q: Give 5 example of integrals yielding natural log functions with solution

A: The integral examples are:

Q: 2x+3) 17. f(x) =- (x² +1)*

A: topic - logarithmic differentiation

Q: Use values of f(x) = In(x) %3D to estimate log ( 6.67 ) using 4th order

A:

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

A: Definition:                                Let f(x) and g(x) be positive for x…

Q: Differentiate. y= log 7x dx log 7x=

A: y=log7xTo differentiate.

Q: Find the derivatives of 20" log(tan x)

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Q: 4. Show that sinh-1 x = log(x + vx² + 1).

A: We have to prove the result.

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

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

Q: Write the derivative of 7 log8(x)

A: We have to find the derivative of 7 log8(x).

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: Differentiate. 10) y = 7X 11) y = 14-X 12) y = log4(2x)

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Q: Find the derivative of the function. h(x) = log4(x + 9) h'(x) =

A: Topic = Derivative