Is there some general formula for deriving an absolut-ed function? Is what I;m doing wrong (a lot of derivation relies on continuous functions, doesn't it?)(adsbygoogle = window.adsbygoogle || []).push({});

IE:

d/dx(abs(sin(x)))

Here's what I got:

abs(x) = x*sign(x)

d/dx(sign(x)) = 0 (x != 0)

therefore

[tex]

\frac{d}{dx}abs(f(x)) = \frac{d}{dx}f(x)*sign(f(x)) = f '(x) * sign(f(x)) + 0

[/tex]

Which, by FTC would mean that:

[tex]

\int cos(x)*sign(sin(x)) \dx = abs(sin(x))

[/tex]

'I checked this by drawing the graphs and it appears right...

Also... I saw that:

[tex]

abs(sin(x)) = sin(x \mod \pi)

[/tex]

[tex]

\int x \mod c \dx = (\int_{0}^{c} x \dx)*INT(\frac{x}{c}) + \int_{0}^{x \mod c} x \dx

[/tex]

example:

[tex]

\int x \mod 1 \dx = INT(\frac{x}{c}) * .5 + x \mod 1

[/tex]

continuing...

[tex]

\int abs(sin(x)) dx = \int sin(x \mod \pi) \dx

= (\int_{0}^{pi} sin(x) dx)*INT(x / \pi) - cos(x \mod \pi)

= 2*INT(\frac{x}{\pi}) - cos(x \mod \pi)

[/tex]

Far as I can tell it works...

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# Derivating absolutes, etc

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