MIT - Massachusetts Institute of Technology

# Definition of the Derivative | MIT 18.01SC Single Variable Calculus, Fall 2010

Definition of the Derivative
Instructor: Joel Lewis
View the complete course: http://ocw.mit.edu/18-01SCF10

License: Creative Commons BY-NC-SA
More information at http://ocw.mit.edu/terms
More courses at http://ocw.mit.edu

#### 24 Comments

• Why did the two variables in the numerator switch in the third step at 7:59? ﻿

• I believe he multiplied the numerator with a common denominator so he can deal with just one fraction instead of two.﻿

• Agreed. I learned the shortcut way from my dad before I actually learned this. It's helpful in math to understand the concepts and theory behind the work rather than just memorizing the steps for finding the solution.﻿

• Nope that is not what I meant. The operators in the numerator switched. Originally it was F(x+delta X ) – F(x), then in step 3 it reversed F(x) – f(x+ delta X) that is how he ended up with a negative solution. ﻿

• at 8:30 why does 1+(x+delta x)^2 = 1-x^2 – 2xdelta x – delta x^2 instead of 1+x^2+2x delta x + delta x^2 ? the signs flipped for some reason… idongitit?﻿

• Why are yuropeons so smug about nothing? This is one of the first things in the class, christ.﻿

• The function f(x)=1/1+x^2 gives for example when x=2 the value y=1/6. It's quite fun.﻿

• You r right. They should get a nobel prize for social service. Tese guys rock. Such a high quality lectures.﻿

• I'm in love with MIT, surely the best institute of all time.﻿

• correct me if i am wrong but you said -x^2 is equal to x^2. I thought only (-x)^2 was equal to x^2. And that -x^2 is the negative of x^2﻿

• anyone can explain to me what is a "recitation" class. My poor English made me think it was a kind of poetry class..:). Do teacher in a recitacion class solve exercises or they are intended to do another activity?. And students in a recitation class?. Thank you very much for answering (if anyone does)﻿

• he didn't say that. Clearly he said "if you replace x by -x…" and that of course implies (x)^2=(-x)^2. Don't get confused with oral language. The word replace is very clear﻿

• your welcome. But I want to ask you something. What is a recitation class. Is it a "practical" class where the teacher solves some exercises?. I've never heard that word. I'll thank you if you explain that to me﻿

• Basically, recitation classes are for courses with a large class size or complicated material (like math or science). Usually these classes will have 1 professor and several student teachers. The professor will teach the large class (also called the Lecture) and cover new material. The student teachers will teach the recitation classes and go over the week's material in more detail.The recitation class gives you the opportunity to address any specific questions or issues ﻿

• The final answer is -2x/(1+x^2)^2. What he wrote after that is just what we were looking for: the derivative of (1/1+x^2)﻿

• in greek schools we learn these and more difficult maths at the age of 17﻿

• Please. What is a TA? Maybe "teaching assistant"? ﻿

• When I was at UConn, the first requirement of a TA was that his/her English skills could be no better than those of a 4 year old with a mouth full of marbles. This is nice.﻿

• I don't understand why there is a negative side value on the graph? Because even if you use negative numbers,the result would still be positive. Am I right?﻿

• beauty and art in every open courseware of MIT. thanks from India.﻿

• That was beautiful! Thank you so much for the deeper explanation. It helped immensely in reinforcing the lecture.﻿