How do you integrate 25e^-x?

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

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Q: Give 1 problem for differentiation rule of exponential

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Q: Solve: ln(x + 2) - ln(4x + 3) = ln (1/x).

A: GivenIn(x+2)-In(4x+3) = In(1/x)We have to solve this equation We have In(x+2)-In(4x+3) = In(1/x)We…

Q: what are differentiation of exponential functions

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Q: Find the second derivative of 1/square root of 2t

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Q: 2X Y=ln (3") +sec (Inx)+tan (ln5x)

A: We will differentiate the function and simplify.   The detailed solution is as follows below:

Q: To get $800 after 212years at 8% compounded continuously

A: $800 after 212 years at 8% compounded continuously.

Q: The half-life of carbon-14 is 5700 years. If an item is discovered with only 17% of the original…

A: Given Half life of carbon-14 =5700 years  i.e. and an item is found with only 17% of the original…

Q: How would I calculate the principle value of  ln(-ie)

A: Given, z=lne-i Convert e-i to polar form. For a complex number a+bi  polar form is given by,…

Q: Find 49 by implicit differentiation if

A: differentiate both sides with respect to p and get the solution in 2nd step.

Q: 1) loga(3-1ogalx-)=2

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Q: 6) In(x²) = (ln x)²

A: These are all unrelated problems since anyone can be solve without any help of another. So by…

Q: The mass reaches 75 grams after t= years.

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Q: find derivative y=square root of (1+ x times e^-2x)

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Q: find the derivativey=log(to the 4th) time (2x Third -6x)

A: To apply the rules for derivative of composite functions

Q: 2. Express in terms of sums and differences of logarithms In 2 3x³y (In 2 divided by 3x³y)

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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: Without showing the details, explain how to condense ln x - 2 ln(x + 1).

A: Given: lnx-2lnx+1

Q: If a Paramecium is about 390 micrometers long, how many centimeters is it? Express in real numbers…

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Q: solve for y: ln(3-y)-ln(y) = 2x + ln(5) without a calculator

A: Given equation is :Moving all the logarithm terms and using the property: ln(a) – ln(b) =…

Q: The half-life of Cesium-137 is 30.7 years. How long will 200 grams of Cesium-137 take to decay to…

A: Given data The half-life of the cesium-137 is t1/2 = 30.7 years. The initial amount of the…

Q: Use logarithmic diffenentiation on an alterative method to findthe derivative of the function?

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Q: If an initial population Po of bacteria doubles in 6 hours, how long will it take to triple (grow to…

A: Given that  6 hours to take doubles the initial population

Q: Determine the derivative of 6x log3(x)

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Q: What are the formulas for differentiation and integration? How to apply those formulas?

A: See the attachment

Q: Find the second-order derivative of the function f(x) = log5 sin x + (2x2 - 8) / (x4 - 4x2). Please…

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Q: Determine how long it will take for an initial investment to double if it earns 7% interest per year…

A: The time take to double the initial investment is approximately 10 years  see the calculation below

Q: Explain the concept of integration and give a real life example.

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Q: Find the derivative OF the exponential funchion y = In ( 5- e **) Please simplify it Further.

A: Consider the provided equation, y=ln5-e4x Find the derivative of the equation. Apply the chain rule…

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

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Q: How to solve for the second derivative?

A: The objective is to solve for the second derivative. Consider a function fx=3x4

Q: A certain radioactive substance decomposes at a rate proportional to the amount present. Of the 1000…

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Q: express ln 3√4 in terms of ln 2 and/or ln 3

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Q: $2000 is invested in an account that pays interest compound continuously, how long will it take to…

A: The answer is given below:

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

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Q: What is something interesting about integrationa and derivatives? Why is it interesting?

A: Given What is something interesting about integration and derivatives? Why is it interesting?

Q: Discuss how the processes of integration and differentiation can be considered as “inverses” of each…

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Q: Find 3rd derivative if ƒ'(x) = x³.

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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: An unknown radioactive element decays into non-radioactive substances. In 880 days, the…

A: The half life of a radioactive element is the time it takes to decay half of its original isotope.…

Q: How is Calculus used to derive the exponential growth or decay model?

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Q: A sample of bacteria taken from a river has an initial concentrationof 2.5million bacteria per…

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Q: Find the accumulated amount after 5 years if $4500 is invested at 4%/year compounded continuously.

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Q: You invest 10,000  and pay 3% interest compound continuously . How will you have in 5 years?

A: Given that You invest 10,000 and pay 3% interest compound continuously .  Now we have to find amount…

Q: Give 5 examples of derivative of exponential function with solution

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Q: In the last 4 line, where is the ^2 in the ln part?

A: The given integral,      ∫13arctanx dx

Q: 7. y= ln 2x³ 5х-3

A: Explanation of the answer is as follows

Q: he radioactive isotope gallium 67 has a biological half-life of 36 hours. If re start with 100…

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Q: what is the Derivative of Exponential Functions?

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