Any mathematicians here?
 

Question:

Something I've never quite understood was the reasoning behind this certain aspect of trig notation:

ex: differentiate sin^3 e^x

The first thing you'd do is rewrite this as (sin e^x)^3 such that you can easily differentiate with the chain rule.

I see this all the time...why is it not just written with the cube applied to whole expression on the outside of the expression to begin with?

Too many profs answer "well that's the way it is". :rolleyes:

simpler to do it the other way (fewer keystrokes) and if it's an agreed upon notation that everyone understands....

sin is a function, and exponentiation is also a function. Every function has to have an argument to work on,

in sin θ, it is clear that sin is the function and θ the argument
in x^n, it is clear that x is the argument and ^3 is the function

In the same way it was traditionally agreed that exponentiation of a trig function can be written sin^n θ or as (sin θ)^n, because mathematicians are basically lazy and don't like to write anything extra


in sin^3, ^3 is not not an argument, it is itself a function w/ sin something as it's argument,

the rewrite is just a clearer way to represent the same thing

^^I was gonna say the same thing, but Bill beat me to it:rolleyes:

Thank you Bill.

Whew! For a minute I thought this was going to be another question about what 48/2(9+3) is again (which everyone knows is 288) :p

Bill is more than just another pretty face !!
;)

Now I know how he can understand all those Porsche transmission graphs. :D

So you don't need parenthesis to clarify?