How to find the derivative of 1/sqrt (x+2) using the chain rule?

Question

mathmale · Answer

You'll find this problem easier if you re-write it first.    1/sqrt (x+2)  should be written as        y = (x+2)^(-1/2).  Can you explain where the (-1/2) came from?

anonymous · Answer

yes you just rewrote the square root and its a negative because the square root is on the bottom.

mathmale · Answer

Yes.  Next preliminary question:  what is the derivative of x+2?

anonymous · Answer

its 1

mathmale · Answer

That's right.  Good.
Now, yo u have  y=(x+2)^(-1/2).  Use the power rule (first) followed by the chain rule (second) to find the derivative.  Have you done this before?  "Power rule with chain rule."

anonymous · Answer

uhm yes. this is what I got. -1/2(x+2)^-3/2

mathmale · Answer

Looks really good, EXCEPT that y ou must enclose the initial -1/2 within parentheses.  Try again, please.  Label your result, remembering that it's a derivative.

anonymous · Answer

(-1/2)(x+2)^-3/2

anonymous · Answer

thanks. I just struggle with rewriting the problem i guess. but thanks for your help!

mathmale · Answer

You're very welcome.  Good luck to you!