# Trig/Chain Rule Derivatives

• Oct 25th 2009, 01:09 PM
VitaX
Trig/Chain Rule Derivatives
I'm just wondering if theres a difference between finding the derivative of $\displaystyle Sin^3(2x+1)$ and $\displaystyle Sin(2x+1)^3$ and if so whats the main difference?
• Oct 25th 2009, 01:10 PM
e^(i*pi)
Quote:

Originally Posted by VitaX
I'm just wondering if theres a difference between finding the derivative of $\displaystyle Sin^3(2x+1)$ and $\displaystyle Sin(2x+1)^3$ and if so whats the main difference?

No because they are one and the same.

$\displaystyle sin^n \theta = (sin \theta)^n \: \: \: \: , \: \: \: n \in \mathbb{Z^+}$
• Oct 25th 2009, 01:11 PM
Jameson
Quote:

Originally Posted by VitaX
I'm just wondering if theres a difference between finding the derivative of $\displaystyle Sin^3(2x+1)$ and $\displaystyle Sin(2x+1)^3$ and if so whats the main difference?

None. They are the same thing just different notation. Writing $\displaystyle \sin^n(x)$ seems to cause less confusion from my experience.
• Oct 25th 2009, 01:15 PM
VitaX
When I input them both on this wolfram site I get different answers

http://www.wolframalpha.com/input/?i=d/dx+%28sin%282x%2B1%29%29^3
http://www.wolframalpha.com/input/?i=d/dx+sin%28%282x%2B1%29^3
• Oct 25th 2009, 01:17 PM
e^(i*pi)
It could be seeing the second one as $\displaystyle sin[(2x+1)^3]$
• Oct 25th 2009, 01:22 PM
VitaX
Well say you have $\displaystyle Sin^2(2x+2)$ and $\displaystyle sin(2x+2)^2$ I thought the difference was the first equation the entire thing is squared but the second equation only $\displaystyle (2x+2)$ is squared. That wrong?