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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- Apr 5th 2009, 12:45 PMment2byoursDerivative
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. . . - Apr 5th 2009, 12:59 PMskeeter
- Apr 5th 2009, 01:04 PMJhevon
alternatively, using the definition of $\displaystyle |x|$, you could realize you have the function:

$\displaystyle

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

$\displaystyle {\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