Question

Why is the derivative of the inverse of f(x) = 1/f'(f^-1(x))?

Answer 1

\[\begin{array}{rcl}
y &=& f^{-1}(x) \\
f(y) &=& x \\
f'(y)y' &=& 1 \\
y' &=& \frac{1}{f'(y)} \\
( f^{-1}(x) )' &=&\frac{1}{f'(f^{-1}(x))}
\end{array}
\]

Answer 2

?You have to use implicit differentiation and the chain rule.

Answer 3

Got it. I was just not seeing that from first glance. Thanks.

Answer 4

This notation might be easier.\[
\begin{array}{rcl}
g(x) &=& f^{-1}(x) \\
f(g(x)) &=& x \\
f'(g(x))g'(x) &=& 1 \\
g'(x) &=& \frac{1}{f'(g(x))} \\
( f^{-1}(x) )' &=&\frac{1}{f'(f^{-1}(x))}
\end{array}
\]

Answer 5

Notation is notation. What math are you in?

Answer 6

super math.

Answer 7

Hehe. He is at Santa Cruiz, so he can go as far as he wants in math there.

Answer 8

I've done as much math as I'm going to do in school. For the most part I've been just refreshing on undergad stuff these days.

Answer 9

Nice I'm a junior in hs so I have a ways to go, but I love calculus. You e?

Answer 10

Definitely planning on an engineering major.

Answer 11

So, you in the grad program? Or just doing something else now that you have all that you need? Cause you really do know your stuff, I have to admit.

Answer 12

I'm looking for a job right now, lol.
Coming to OS so that I don't forget everything though.

Answer 13

Yah, I am using OS to help refresh some skills, help people (which is fun), and learn more. I have pretty much the math I need, but I want to learn more for enrihment.

Answer 14

What level are you at e?

Answer 15

Right now I am taking a linear algebra class. Not needed for my comp sci degree, but it is good for coding.

Answer 16

Man this summer I'm tying myself to my CPU and gonna learn how to code. It seems that for any math science guy it's a must. What languages would you recommend first?

Answer 17

The majors for initial learning and long term use are Python, PHP, Java, and C++.

Answer 18

JavaScript? I'm more interested in applications than just web coding as I plan to start doing some cad sketches.

Answer 19

What about Haskell? I know that's long term, but what is it for.

Answer 20

Down the road rather

Answer 21

I did not say JavaScript. I said Java. Different animal. The Andoid uses Java as the main front end language, C++ as back end, making it a prime candidate for usefulness long term.

Answer 22

I know the difference I'm just asking you about it as it seems to be one that is always recommended to newcomers

Answer 23

This web site, google, and many, many others are now all based in Python. A language that has truly come of age and is used by MIT for engineering projects. Heck, the self driving car uses Python.

Answer 24

Doesn't Android use C as a back-end, since the Linux kernel is written in C?

Answer 25

LINUX is not pure C any more, from what I have seen. And the Android toolkit I got, if I reall, was C++.

Answer 26

What about perl? I have heard some about perl in the same frame as python, but going off your earlier comment python definitely seems to be a must

Answer 27

NDK, Native Development Kit: http://developer.android.com/tools/sdk/ndk/index.html
C and C++. Whee.

Answer 28

Perl is used by hackers who are trying to break some system and have no intention of writing elegant maintainable code.

Answer 29

Perl is one of tose languages that seemed like it was going to really go, then some of the core developers fell in love with Python, including the founder of Perl. LOL. So things sort of shifted that way. Plus, many of the things that gave power to Perl were done in C, so people had these odd mismashes of things. Where as Python did it all in house.

This does not mean Perl is bad. It is just not as common as it was when Python was a fledgling. The Google/Stanford/MIT adoption of Python is what really shot it up over the top for popularity in coders.

Answer 30

Functional languages are used by semantic purists who are stuck in academic limbo. It's good to try it out though.

Answer 31

That is what Python started as. It was a training tool language. But one of the students saw potential with it, so he revised it into a full bore language. But he had a sense of humor, so he dd all the examples with Eggs and Spam, and named the thing Python after the people that popularized jokes about Eggs and Spam.

Answer 32

Though I've heard little about coding, I've heard that everyone has been trying to make their own language, but in the end they only get c love children

Answer 33

Some are Tyrion lanisters others not so much

Answer 34

Jon snows rather

Answer 35

Well, the need for truly new languages is questionable at best. So many have been tossed out and 90% have died. And that is just if you talk about the well developed ones. If you talk hoby-horse, I bet it is 99.99% died.

Answer 36

Alright man I'm out thanks for the help and advice

Answer 37

Try this: Free college class that takes a practical method to teaching Python.
http://www.pythonlearn.com/

Answer 38

And by college, I mean the prof of the college class made his online version and book free.

Answer 39

I really like Javascript.

Answer 40

But there are parts of it I don't like at all.

Answer 41

Java is an OK language, with the practical advantahe that you learn much of JavaScript at the same time. Reverse is also true. My main problem with Java is that it seems to be a bit of a memory hog, and some of the scripts tend that way. Especially bad AJAX implementations.

Answer 42

You learn Javascript learning Java? How?

Answer 43

Great thing about JavaScript: Everyone can run it.

Answer 44

So long as they have a browser.

Answer 45

That's why everyone's told me to learn it

Answer 46

I wouldn't mind if Dart got popular though.

Answer 47

But what is the purpos for Haskell?

Answer 48

Purposes

Answer 49

I watched the first two videos of that PythonLearn and was very impressed. He wants to get people to where they are not truly programmers, but they are able to just do things with code. That tells me he is aiming for the fun parts, development, more than the dry parts, technical aspects of being a programmer.

Answer 50

Haskell is another functional language. It's something you learn for fun.

Answer 51

http://en.wikipedia.org/wiki/Purely_functional

Answer 52

But not many really use it, it's just more of a show of bravado?

Answer 53

Ever try prolog? lol

Answer 54

No, there are people that believe functional is 100% the way to go. So they find a favorite functional language and use it. This has resulted in some amazing developmets from functional programmers... but most do not see it as being practical for everything, so they stick with a wider reaching language.

Answer 55

Prolog... hehe. Let me put it to you this way... I started with ROM BASIC because it was all I had and it was required. I am going back to school for coding these days, but was mostly admin and tech work for years, so I am having to relearn a lot of coding stuff.

Answer 56

Which is why I know a lot about the history of perl... it being the primary cgi language until things like Java and PHP came into power.

Answer 57

Thanks again peace

Answer 58

np. Have fun!