Using logarithmic differentiation

[rteng]

using logarithmic differentiation I can get it to a point where I have...

ln(y)=20[ln(x+sqrt(x))-ln(x^2-2^x)]

I do not know what to do at that point

 

[rocomath]

just take the derivative as you normally would

also you will have $$\frac{y'}{y}= ...$$

bring Y to the other side and plug in what Y is. the rest is straight forward differentiation.

 

[rteng]

yeah but then you have a term that is:

[1/(x^2-2^x)]*(2x-d/dy2^x)

thats where I get stuck

 

[rocomath]

i'm not really following

you mean on the $$x^{2}-2^{x}$$ part? how would you take it's derivative?

 

[rteng]

$$y=((x+sqrt(x))/x^{2}-2^{x})^{20}$$

$$lny=20(ln(x+sqrt(x))-ln(x^{2}-2^{x}))$$

$$y'/y=(20/(x+sqrt(x))*(1+1/2(x)^{-1/2}))-(20/x^{2}-2^{x})*(2x-derivative of 2^x)$$

 

[rteng]

yes that part sorry