# Chain Rule Application

• October 27th 2009, 12:08 AM
VitaX
Chain Rule Application
Find the derivative of $Sec^2(x+2)^3$

$y' = 2Sec(x+2)^3(Sec(x+2)^3)(tan(x+2)^3)3(x+2)^2(1)$

$6Sec(x+2)^3(Sec(x+2)^3)(tan(x+2)^3)(x+2)^2$

My question is when you multiply $Sec(x+2)^3$ and $Sec(x+2)^3$ would your answer be $Sec^2(x+2)^3$ or $Sec(x+2)^6$
• October 27th 2009, 12:14 AM
ramiee2010
Quote:

Originally Posted by VitaX
My question is when you multiply $Sec(x+2)^3$ and $Sec(x+2)^3$ would your answer be $Sec^2(x+2)^3$ or $Sec(x+2)^6$

$\sec(x+2)^3 \cdot \sec(x+2)^3=\{\sec(x+2)^3 \} ^2=Sec^2(x+2)^3$
• October 27th 2009, 12:15 AM
VitaX
Quote:

Originally Posted by ramiee2010
$\sec(x+2)^3 \cdot \sec(x+2)^3=\{\sec(x+2)^3 \} ^2=Sec^2(x+2)^3$

I thought so. So the final answer is

$6 Sec^2(x+2)^3(tan(x+2)^3)(x+2)^2$