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dqs 11/11/24

shea7651 · 2024-11-11T19:07:33.807Z

1. (q)Summarize the main points from the review on prokaryotes and eukaryotes. How do these points help in understanding cellular evolution? 2. (a)eukaryotes evolved from simpler prokaryotic ancestors with the development of a nucleus and organelles being a significant step in cellular evolution 3. (q)in the following discussion and solutions the derivative of a function h(x) will be be denoted by D{h(x)} or h'(x) the quotient rule is a formal rule for differentiating problem's where one function is divided by another it follows from the limit definition of derivative and is given by D{f(x)/g(x)} = [g(x)f'(x)-f(x)g'(x)]/[{g(x)}^2 remember the rule in the following way always start with the ''bottom" function and end with the ''bottom" function squared. note that the numerator of the quotient rule is identical to the ordinary product rule except that subtraction replaces addition in the list of problems which follows most problems are average and a few are somewhat challenging differentiate g(x) = [1+ln(x)]/[(x^2)-ln(x)] 4. (a)[1-(x^2)-(2x^2) ln(x)]/[x((x^2)-ln(x))^2] 5. (q)what's your favorite sandwich 6. (a)ham and cheese 7. (ps q = question and a = answer)

in General Class Discussions

(q)Summarize the main points from the review on prokaryotes and eukaryotes. How do these points help in understanding cellular evolution?
(a)eukaryotes evolved from simpler prokaryotic ancestors with the development of a nucleus and organelles being a significant step in cellular evolution
(q)in the following discussion and solutions the derivative of a function h(x) will be be denoted by D{h(x)} or h'(x) the quotient rule is a formal rule for differentiating problem's where one function is divided by another it follows from the limit definition of derivative and is given by D{f(x)/g(x)} = [g(x)f'(x)-f(x)g'(x)]/[{g(x)}^2 remember the rule in the following way always start with the ''bottom" function and end with the ''bottom" function squared. note that the numerator of the quotient rule is identical to the ordinary product rule except that subtraction replaces addition in the list of problems which follows most problems are average and a few are somewhat challenging differentiate g(x) = [1+ln(x)]/[(x^2)-ln(x)]
(a)[1-(x^2)-(2x^2) ln(x)]/[x((x^2)-ln(x))^2]
(q)what's your favorite sandwich
(a)ham and cheese
(ps q = question and a = answer)

1 comment

Comments (1)

Constance Quigley

Nov 30, 2024

Thank you for your contributions to the discussion. Below are my responses to your inquiries:

1. Cellular Evolution: Your point on the evolution of eukaryotes from prokaryotes is spot on. The development of organelles like mitochondria (via endosymbiosis) is a fascinating evolutionary leap. This transition was pivotal for multicellular organisms and the complexity of life.
2. Quotient Rule Application: The differentiation of \[ D\{g(x)\} = \frac{1 - (x^2) - (2x^2) \ln(x)}{x\left(x^2 - \ln(x)\right)^2} \] demonstrates a solid grasp of the quotient rule, though your final derivative result may have a minor discrepancy in the numerator. If you'd like, we can re-check the differentiation process step-by-step to ensure accuracy.
3. Sandwich Choice: Ham and cheese on a fresh, warm croissant is indeed a classic and delightful choice—simple, yet satisfying.

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