- #1

- 334

- 1

I'm looking for a little guidance in solving the derivative y'(x)of the following function containing an absolute in the exponent:

[tex]y(x)=e^{a|x|}[/tex]

I'm pretty sure its not as simple as

[tex]y'(x)=a e^{a|x|}[/tex]

Any suggestions??

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- Thread starter robousy
- Start date

- #1

- 334

- 1

I'm looking for a little guidance in solving the derivative y'(x)of the following function containing an absolute in the exponent:

[tex]y(x)=e^{a|x|}[/tex]

I'm pretty sure its not as simple as

[tex]y'(x)=a e^{a|x|}[/tex]

Any suggestions??

- #2

- 246

- 1

[tex]\partial_x e^{a|x|} = \partial_x e^{-ax} = -ae^{-ax} [/tex]

for [tex]x>0[/tex] you get

[tex]\partial_x e^{a|x|} = \partial_x e^{ax} = ae^{ax} [/tex]

combining these could be

[tex]\partial_x e^{a|x|} = sign(x) a e^{a|x|} = \frac{x}{|x|} a e^{a|x|}[/tex]

but remember that it is not defined in 0.

- #3

- 334

- 1

so the [tex]\frac{x}{|x|}[/tex] is really just a neat way of setting the coefficient to [tex]\pm 1[/tex], depending on where x is.

Thats cool. :)

Thanks mranderson, very helpful.

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