1. ## Chain Rule Application

Find the derivative of $\displaystyle Sec^2(x+2)^3$

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

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

My question is when you multiply $\displaystyle Sec(x+2)^3$ and $\displaystyle Sec(x+2)^3$ would your answer be $\displaystyle Sec^2(x+2)^3$ or $\displaystyle Sec(x+2)^6$

2. Originally Posted by VitaX
My question is when you multiply $\displaystyle Sec(x+2)^3$ and $\displaystyle Sec(x+2)^3$ would your answer be $\displaystyle Sec^2(x+2)^3$ or $\displaystyle Sec(x+2)^6$
$\displaystyle \sec(x+2)^3 \cdot \sec(x+2)^3=\{\sec(x+2)^3 \} ^2=Sec^2(x+2)^3$

3. Originally Posted by ramiee2010
$\displaystyle \sec(x+2)^3 \cdot \sec(x+2)^3=\{\sec(x+2)^3 \} ^2=Sec^2(x+2)^3$
I thought so. So the final answer is

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