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Thread: Chain Rule Application

  1. #1
    Member VitaX's Avatar
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    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 $\displaystyle Sec(x+2)^6$
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  2. #2
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    Quote Originally Posted by VitaX View Post
    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 $\displaystyle Sec(x+2)^6$
    $\displaystyle \sec(x+2)^3 \cdot \sec(x+2)^3=\{\sec(x+2)^3 \} ^2=Sec^2(x+2)^3$
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  3. #3
    Member VitaX's Avatar
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    Quote Originally Posted by ramiee2010 View Post
    $\displaystyle \sec(x+2)^3 \cdot \sec(x+2)^3=\{\sec(x+2)^3 \} ^2=Sec^2(x+2)^3$
    I thought so. So the final answer is

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