Understanding Differentiation with x: ln and Exponents

[M.Qayyum]

Homework Statement

1) ln { (x^2+x+1) / ( x^2-x+1) } here ln = natural log
2) x^2+x^(2y)=c here c=constant

Homework Equations

The Attempt at a Solution

 

[Mark44]

Show us your attempt at a solution.

 

[M.Qayyum]

Show us your attempt at a solution.

My attempt at 2)

x^2+x^(2y)=c

x^2+2ylnx=c

diff wrt x

2+(2lnx+1/x.2y.y')=0

1/x.2y.y'=-2-2lnx

y'= -2(lnx+1)x / 2y

is this correct and i can't understand the question no. one and how to start it's differentiation.

 

[Mark44]

My attempt at 2)

x^2+x^(2y)=c

x^2+2ylnx=c

x^2y \neq 2y ln(x).

You can write x^2y as (eln(x))^2y = e^{2y ln(x)}, and then differentiate.

For #1, ln(a/b) = ln(a) - ln(b). Use that property of logs before trying to differentiate.

diff wrt x

2+(2lnx+1/x.2y.y')=0

1/x.2y.y'=-2-2lnx

y'= -2(lnx+1)x / 2y

is this correct and i can't understand the question no. one and how to start it's differentiation.

 

[M.Qayyum]

Thank u very much...it really helps