My very brilliant mathematician niece is at some high-falutin’ “math camp” thing at college, where she gets paid big bucks to sit around for seven weeks this summer thinking about mathy things that apparently have no practical applications at this time but might include algorithms to be used for cell phones and applying coatings to various manufactured goods…I think. Those were the words I understood. All I know is it is very prestigious and intense and exclusive. I was an English education major. We no longer speak the same language.
So today she posted this joke, and I of course don’t get it, and neither does her dad (my brother), though her math teacher mom probably does and her twin claims to vaguely remember it. Anyhow, I’d like to understand the humor here, so could anyone please translate this for someone who did very well in math back in high school, but not at this level and for pity’s sake I graduated back in 1975!
Here’s the joke:
All of the functions are at some party. Suddenly the door opens and derivative enters. All of the functions start running outside and shouting, “He’s going to derivate me! He will!!” Only one function stays put and looks around smirking.
Derivative comes up to the function and asks,“Why aren’t you running away?”
It answers, “I’m e^x! I don’t need to be scared of you!”
The derivative laughs and replies, “I’m d/dy.”
I’m not sure what level of Math you are comfortable with (I’m going to assume you know algebra) but I’ll give it a shot.
when you derive most functions (essentially calculate the rate at which the expression changes as x changes) the solution tends to be of a smaller order than you started with, and eventually turns to 0 if you keep deriving each solution. for example x^3 when derived (denoted d/dx which means derived with respect to x) becomes 3x^2, which becomes 6x then 6 then 0. e^x is a special function in that when derived its rate of change is exactly e^x. No matter how many times you derive the solution with respect to x (meaning apply d/dx) it will never change.
In the case of the joke the e^x function wasn’t afraid of the derivative because it thought it was safe from being reduced. It turns out that the derivative wasn’t deriving with respect to x, but with respect to y (d/dy). When you derive a function with no y variable in it with respect to y, it instantly turns to 0, as the function does not change at all no matter what the value of y is. So while the e^x function thought he was safe from the derivative, he will actually be turned to 0 very quickly.
I hope I haven’t sucked all of the entertainment value out of the joke for you.
I apologize if I have explained anything poorly, but this is my understanding of it.
I’m sure someone will be around shortly to correct me if this is the case.
For the purposes of the joke, yes. For functions that contain a y variable no.
(when d/dy is applied to y^3 it becomes 3y^2 not 0, because that expression will change depending on the value of y)
In simpler calculus d/dx is used almost exclusively so for many purposes when saying derive you would assume d/dx, not d/dy which is why the function in the joke thought he was safe.
And Kittenblue, you’re doing great just REMEMBERING the joke; I didn’t understand a word of it and couldn’t repeat it even now that I’ve been told the answer.
That’s not true if x is a function of y*. Then (d/dy) e[sup]x[/sup] = e[sup]x[/sup] (dx/dy). If x and y are independent, of course, dx/dy = 0 and the exponential’s fears at the end are justified.
*although the usual usage is y being a function of x. But there’s no reaso n it couldn’t be the other way around. Theyre just labels.
