Question

Dervative question involving ln

Answer 1

\[Trying \to determine derivate of \ln x \sqrt{x^2-6}\]

Answer 2

I get ln x = 1/x

Answer 3

added to \[1/2\ln x^2-6\]

Answer 4

Do I also need to include the derivative of x^2 - 6?
Which is 2

Answer 5

\[\Large\bf\sf \left(\ln x\sqrt{x^2-6}\right)'\]Is the sqrt inside of the log as well?

Answer 6

yes
Sorry.

Answer 7

I take that back. No it is not

Answer 8

heh

Answer 9

So I guess we'll have to start with `product rule`.\[\Large\bf\sf \left(\ln x\sqrt{x^2-6}\right)'=\color{royalblue}{\left(\ln x\right)'}\sqrt{x^2-6}+\ln x\color{royalblue}{\left(\sqrt{x^2-6}\right)'}\]

Answer 10

We need to take the derivative of \(\Large\sf \color{royalblue}{\text{these parts}}\).

Answer 11

(1/x) (sqrtx^2-6) + (lnx) (1/2) (2x^-1/2)

Answer 12

Mostly good.
Ok we just need to remember our chain rule when we differentiate the sqrt (since the inner function is more than just `x`).