Question

Derivative of Exp[Abs[x]]?

Answer 1

So we need to find this derivative?\[\Large \left(e^{|x|}\right)'\]

Answer 2

yes

Answer 3

Hmm I guess we would follow the normal rule for derivative of an exponential and then follow it up with the chain rule.\[\Large \left(e^{|x|}\right)'\quad=\quad e^{|x|}\color{royalblue}{\left(|x|\right)'}\]

Answer 4

(d/dx) (Abs[x]) =+-1?

Answer 5

depending on x?

Answer 6

\[\Large \frac{d}{dx}|x|\quad=\quad \frac{d}{dx}\sqrt{x^2}\quad=\quad \frac{x}{\sqrt{x^2}}\quad=\quad \frac{x}{|x|}\]

Answer 7

But ya if we write out specific intervals of x, we could get rid of the absolute bars. That might look a little better.

Answer 8

is by definition Abs[x] = Sqrt[x^2]?

Answer 9

Ya, that's a good one to remember probably c:

Answer 10

thank you, you have been very helpful! have nice day!