Question

Need help taking this derivative, will write the equation below

Answer 1

\[\sqrt{\left| x \right|}+x/10\]

I understand how to take this derivative when x is positive, but what about when x is negative?

Answer 2

\[\frac{ d }{ dx }\left| f \left( x \right) \right|=\frac{ f \left( x \right) }{ \left| f \left( x \right) \right| }f \prime \left( x \right)\]

Answer 3

Hmm, idk what to do with that.

Answer 4

\[\frac{ d }{ dx}\sqrt{\left| x \right|}=\frac{ d }{ dx }\left( \left| x \right| \right)^{\frac{ 1 }{ 2 }}=\frac{ 1 }{ 2}\left( \left| x \right| \right) ^{\frac{ -1 }{ 2 } }\frac{ d }{ dx }\left| x \right|\]

Answer 5

can you solve further ?

Answer 6

Possibly, so is \[\left| x \right| = \sqrt{x ^{2}}\] ?

And I just solve it this way?

Answer 7

\[\frac{ d }{ dx }\left(\sqrt{x^2} \right)=\frac{ d }{ dx }\left( x^2 \right)^{\frac{ 1 }{ 2 }}=\frac{ 1 }{ 2 }\left( x^2 \right)^{\frac{ -1 }{ 2 }}2 x=\frac{ x }{ \left( x^2 \right) ^{\frac{ 1 }{ 2 }} }=\frac{ x }{ \left| x \right| }\]