Differentiate (answers not to be simplified)

[ttpp1124]

Homework Statement

I differentiated the following questions; however, I don't know if I simplified any of them..

Relevant Equations

n/a

Thank you in advance :)

 

[Mark44]

Homework Statement:: I differentiated the following questions; however, I don't know if I simplified any of them..
Relevant Equations:: n/a

View attachment 261567
Thank you in advance :)

There a couple errors. Parts a), c) and d) are fine, but b) has an error.
For b) in the 2nd line of your work you have 2x in the numerator. It shouldn't be part of that fraction. I think you also have a sign error when you used the quotient rule.

 

[Mark44]

Also, in the future, please post only one, or at most two, problems at a time. Squeezing so much writing in a relatively small space makes it hard for some of us to read.

 

[ttpp1124]

Also, in the future, please post only one, or at most two, problems at a time. Squeezing so much writing in a relatively small space makes it hard for some of us to read.

Thank you for reviewing my work. I'm sorry for cramming the questions together, will submit separate questions next time!

 

[berkeman]

(answers not to be simplified)

Just curious -- why would that be part of a math problem statement? Is that some standard format for some types of math classes or problem types? I don't think I've seen that before. Thanks.

 

[Mark44]

Just curious -- why would that be part of a math problem statement? Is that some standard format for some types of math classes or problem types? I don't think I've seen that before. Thanks.

Not simplifying makes it easier for the grader to see that the differentiation was done correctly. If the result had been further simplified, the grader couldn't tell that an incorrect answer was the result of an error at the differentiation step or later as an algebra error.

 

[LCKurtz]

How else to get students through calculus who can't do algebra?

 

[sysprog]

Cheap, fast, and reliable. Pick any two.

I like your sigline -- it reminds me of an adage about alcohol -- there's too much, too often, and too long -- pick any two and you might get away with that, at least for a while, but you can't get away with all 3 -- well, we're all mortal to begin with, but let's please make that later, rather than sooner, if we can.

 

[epenguin]

Also, in the future, please post only one, or at most two, problems at a time. Squeezing so much writing in a relatively small space makes it hard for some of us to read.

re ease of reading please see also my comment in https://www.physicsforums.com/threads/given-y-u-2-1-2u-1-and-u-2x-3-3x-find-dy-dx.988146/

 

[sysprog]

How else to get students through calculus who can't do algebra?

Well, maybe teach them how to count things one-by-one, and then patiently wait for them to get impatient -- that shouldn't take too long -- then show the rapid road . . .

 

[berkeman]

Not simplifying makes it easier for the grader to see that the differentiation was done correctly. If the result had been further simplified, the grader couldn't tell that an incorrect answer was the result of an error at the differentiation step or later as an algebra error.

Back in undergrad, I worked the summer between my junior and senior years for Tektronix up in Oregon. Another EE student who was one year behind me also worked at Tek that summer, and we were roommates that summer and became friends. He was a super-bright math prodigy (with a very practical EE side), and he regularly competed in and won major math competitions.

I was a TA the next year in a class that he happened to be taking, so I ended up grading some of his homework assignments. The policy was always to take off points when a student did now show adequate intermediate steps in their work, on the assumption that they were just cheating by copying down the answer from somewhere else. But when any of us graders saw Dan's papers with basically no work shown, he always got 100% credit for correct answers, since he was well known to do complex problems and calculations in his head. LOL

 

[sysprog]

Back in undergrad, I worked the summer between my junior and senior years for Tektronix up in Oregon. Another EE student who was one year behind me also worked at Tek that summer, and we were roommates that summer and became friends. He was a super-bright math prodigy (with a very practical EE side), and he regularly competed in and won major math competitions.

I was a TA the next year in a class that he happened to be taking, so I ended up grading some of his homework assignments. The policy was always to take off points when a student did now show adequate intermediate steps in their work, on the assumption that they were just cheating by copying down the answer from somewhere else. But when any of us graders saw Dan's papers with basically no work shown, he always got 100% credit for correct answers, since he was well known to do complex problems and calculations in his head. LOL

I remember in the '70s telling a guy to 'use the Tektronix', even though it had an orange screen, when he wanted to show a rotatable cube . . .