Quote:
Originally Posted by BGCarrera32
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".  |
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