# Quick question

i got this question from a friend and its bugging me because i cannot understand it. i just cannot understand what it means... here is it, word for word what i have on the assigned paper

"if f(x) = x^n , "n" is a positive interger, the first derivative of f(x) which is identically zero is "

A) the nth
B) the (n-1)st
C) the (n+2)nd
D) the first
E) the (n+1)st

those are the options...am I to assume that its so easy that its B? i am hesitant to pick B tho because this teacher is known for his tricks and it seemed a little too easy...a little help would be great for my friend and myself

## Answers and Replies

Tide
Science Advisor
Homework Helper
I suggest trying a few simple example like $x^2$ and so forth - you should see a pattern emerge! :)

Basically, it takes n iterations to get to a constant, and then one more.

Not sure if you got this already, but the question is asking "How many times do you need to differentiate this thing to get 0?"

It's worded in a tricky manner, but essentially, what do you know about differentiating a constant? How many times will you need to differentiate to get a constant? Then, how many times will you have to differentiate that to get 0?

PS - please use more descriptive thread titles. I've noticed a few threads by you with no indication as to what lies within. It makes it very difficult to get help when you need it if people skip over it!

The answer is n+1 times

The hint lies in the fact
The nth differential of f(X)=x^n gives a constant
And n+1th diffrential i.e of a constant gives us Zero

Remember that each time you take de derivative, the exponent reduces by one.
And the derivative of a constant is zero.
Ciao