Question

derivation of ln(sqrt(x^2-7))

Answer 1

http://www.wolframalpha.com/input/?i=derivation+of+ln%28sqrt%28x%5E2-7%29%29

When it becomes 1/2(sqrt(u)) how does it cancel into (x^2-7) instead of just 1 (x^2-7)?

Answer 2

First you can rewrite this using properties of log
It will be tons easier
ln(u^r)=r ln (u) is a hint

Answer 3

acutally, I think I get it...

Answer 4

we do a flip so it's the sqrt's x each other to be a normal x^2-7

Answer 5

\[\frac{d}{dx}(\ln(\sqrt{x^2-7)})=\frac{d}{dx}(\ln(x^2-7)^\frac{1}{2})=\frac{1}{2} \frac{d}{dx}(\ln(x^2-7))\]

Answer 6

Tons easier than what wolfram did

Answer 7

Yeah it is, I forgot about log properties :)