HELP!!!!!
let f(x)=lnsqrt((4x+6)/(9x+6)) find f'(x)

Question

HELP!!!!!
let f(x)=lnsqrt((4x+6)/(9x+6)) find f'(x)

zugzwang · Answer

$$f(x)=\ln \sqrt{\frac{4x+6}{9x+6}}$$
Is this it?

anonymous · Answer

Yes

zugzwang · Answer

Chain rule, do you know it?

anonymous · Answer

not very well in this problem I tried doing the quotient rule at first and epicaly failed

zugzwang · Answer

Ok, chain rule, as best as I can say it, first, try to determine the outermost function...
In this case, it's ln, right?

anonymous · Answer

yes and  the derivative of that is 1/x

zugzwang · Answer

That's right.  So whatever is inside the ln, just treat it as one big x.
So you have
$$\frac{1}{\sqrt{\frac{4x+6}{9x+6}}}$$

zugzwang · Answer

We're not yet done, ok, this is just part of the process...

anonymous · Answer

So then would you apply the quotient rule to what is under the radical?

zugzwang · Answer

No, now that you've pretty much done away with the "ln" part, now, what is the outermost function? It's the square root, right?  What's the derivative of a square root?

anonymous · Answer

1/2(4x+6/9x+6)^-1/2

zugzwang · Answer

That's right, and you multiply that to that other fraction we had a while ago.  We're not yet done.  Now what's the outermost function? It's the rational function, the (4x+6)/(9x+6), just get the derivative of that, and multiply it to the ones we already got, and you're done :)

anonymous · Answer

so for that inside we do use the quotient rule correct?

zugzwang · Answer

Yes, that's when you use the quotient rule.