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Math Help - Derivative

  1. #1
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    Derivative

    What is the derivative of (sin|x|)^3?

    -for x>0
    -for x<0

    I think it is 3sin|x|*(cos|x|) for the first and 3sin|x|*(-cos|x|) for the second but I'm not sure. . .
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  2. #2
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    Quote Originally Posted by ment2byours View Post
    What is the derivative of (sin|x|)^3?

    -for x>0
    -for x<0

    I think it is 3sin|x|*(cos|x|) for the first and 3sin|x|*(-cos|x|) for the second but I'm not sure. . .
    \frac{d}{dx}(\sin|x|)^3 = 3(\sin|x|)^2 \cdot (\cos|x|) \cdot \frac{x}{|x|}

    if x > 0 , |x| = x

    if x < 0 , |x| = -x
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  3. #3
    is up to his old tricks again! Jhevon's Avatar
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    alternatively, using the definition of |x|, you could realize you have the function:
    <br />
f(x) = \left \{ \begin{array}{ll} (\sin x)^3 & \text{ if } x > 0 \\ (\sin (-x))^3 & \text{ if } x < 0 \end{array} \right.

    {\color{white}f(x)} = \left \{ \begin{array}{ll} (\sin x)^3 & \text{ if } x > 0 \\ -(\sin x)^3 & \text{ if } x < 0 \end{array} \right.

    now differentiate piece by piece
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