What is the difference between total derivative, total differential and exact differe...?

Let's look at a real-valued function of several variables: [math]f:\mathbb{R}^n\to \mathbb{R}[/math] [math]f=f(x_1,x_2,\ldots,x_n)[/math] Such functions can model a wide variety of physical, …

Top stories for Long   What is the difference between total derivative, total differential and exact differential? Alon Amit, PhD in Mathematics; Mathcircler. • Updated April 3, 2019 Let's look at a real-valued function of several variables: [math]f:\mathbb{R}^n\to \mathbb{R}[/math] [math]f=f(x_1,x_2,\ldots,x_n)[/math] Such functions can model a wide variety of physical, mathematical or economical phenomena, and much else besides. ... Read more » 185 8   Why does Linux not "just work" like Windows? Franklin Veaux, Technology enthusiast, mad engineer, and tech startup founder. • Answered September 16 Linux is not an operating system. Linux is a religion. Like all religions, it has schisms, holy wars, prophets, sectarian violence, and the Linux distro tree looks a lot lik... Read more » 784 90   Why haven't drastic predictions about climate change, like the disappearance of places like Florida, come true yet? Bruce, Business Intelligence Consultant (2000-present) • Updated Mon About ten years ago a climatologist answered a question on Quora along the lines of "When will Key West be submerged by sea level rise?" His answer was that that wouldn't h... Read more » 2.7K 532   Somebody lied to me. I was told so many times that tariffs would crash our economy and the stock market and our country would be destroyed. Now we are at record highs in the stock market and our economy is thriving. Who lied to me? Gordon Strathdee, lived in The United States of America (1992-1996) • Updated 21h ago Yes, you are absolutely right. You were lied to and personally I think it's a disgrace. What sort of person engages in such foul dishonesty? My advice, is to track that per... Read more » 8.4K 1.1K   What was the reason for the closure of the Woodhead Tunnel? Nicholas Stone, Life long interest in trains. • Answered August 3 Three 4.8 km Woodhead Tunnels are still in use - carrying high voltage cables under the Pennines rather than carrying trains. They are owned and operated by the National Gr... Read more » 97 7   When a surgeon opens up a person with cancer, what does that cancer look like? Jim Finnis, Soft tissue sarcoma survivor • Updated March 15, 2020 I asked my surgeon this question after the operation as all I had seen was this big lump in my leg. I was curious about what the thing in there actually looked like. She sa... Read more » 1.6K 149   Did the passengers in the back of the 9/11 planes see it crumple on impact? Dominic DiPentino • Answered September 14 No. The reason is this: the speed at which these planes were flying prevented that. Once the noses of the aircraft's touched their destination, the passengers in the rear o... Read more » 2.7K 285   I can run 2 miles in just under 9 minutes. When I get to Army basic training and take my PT test, should I run the 2 mile in under 9 or blend in with the other soldiers and not stand out? Doug Freyburger, lived in Austin, TX • Updated August 29 "I can run 2 miles in just under 9 minutes. When I get to Army basic training and take my PT test, should I run the 2 mile in under 9 or blend in with the other soldiers an... Read more » 2.9K 343   Why hasn't Vladimir Putin asked China to send Chinese troops to Ukraine since they are close allies and the war would be over very quickly? Asked in Russia 🇷🇺 and Ukraine 🇺🇦 conflict • Answered by Imants Liepiņš • September 17 Recently I was staying 10 days in Nanjing and had chances to talk with many different Chinese people about many topics, including Chinese views on world affairs (of course,... Read more » 1.3K 152   If being publicly intoxicated is illegal, how could one ever legally leave a bar and walk home? Bart Crunk, former Analyst (retired) (1991-2021) • Answered March 20, 2023 You can't. I used to live in a small town. A lot of the bars and clubs had back entrances that lead to an alley. The cops would sit at the end of the alley and pop people f... Read more » 1.2K 223   Can multiplication of two numbers equal zero if neither of them is zero? Alex Eustis, Ph.D. Mathematics, University of California, San Diego (2013) • Updated July 21 You have to understand that the answer to this question depends exactly on what you mean by "number", and nothing else. The property that [math]ab=0[/math] implies ([math]a=0[/math] or [math]b=0[/math]) is known as the "zer... Read more » 101 7   Japan is such a well run country. People are courteous, nice, and not aggressive and in such a hurry. Why can't America and American cities be like that? Anne Agard, old woman • Answered September 13 I lived and worked in Japan for several years in the 1970s. The culture is profoundly different. I will share a few things I observed that gave me insight. I saw parents tell... Read more » 1.1K 104 Read more in your feed

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