I need help with 3 more derivative problems if someone is willing to help!

Question

margotlakus · Answer

$$y=\frac{ (x+1)(x-2) }{ (x-1)(x+2) }$$    &    $$x > 2$$

margotlakus · Answer

$$\sqrt{x}+\sqrt{y}=9$$   y(1)=64   find y'(1) by implicit differentiation

margotlakus · Answer

$$\frac{ y }{ x-6y }=x^4-8$$ at the point $$(1,\frac{ 7 }{ 41 })$$

margotlakus · Answer

$$\frac{ x^2 }{ 49 }+\frac{ y^2 }{ 16 }=1$$  y(3)=3.61403161   y'(3)

jackthegreatest · Answer

do you know the quotient rule?

margotlakus · Answer

I do but I have to use logarithmic differentiation

jackthegreatest · Answer

ohh, i have not reached there in my math class yet : ( sorry

tkhunny · Answer

Okay, have you considered introducing the logarithm, then using a few log rules to manipulate?

margotlakus · Answer

I really have no idea what to do...

tkhunny · Answer

$y = \dfrac{(x+1)(x-2)}{(x-1)(x+2)}$

Introduce the logarithm.

$log(y) = log\left[\dfrac{(x+1)(x-2)}{(x-1)(x+2)}\right]$

Use some log rules to expand or simplify and show your best implicit derivative methodology.

margotlakus · Answer

Is that the derivative or

tkhunny · Answer

Did you read it?  I introduced the logarithm and told you to find the derivative.  Does that mean it's the derivative or is there some work for you?

margotlakus · Answer

Oh, nevermind. Sorry my mind is very tired.

tkhunny · Answer

You can do it.  Use your log rules.  log(ab) = log(a)+log(b) and log(a/b) = log(a) - log(b).  Those guys.

margotlakus · Answer

I need help with the other problems if anyone is willing

mathmale · Answer

Unsure of which problem you want help with.  Avoid this ambiguity by posting just one problem at a time.