Use logarithmic differentiation to find derivative

[dubb]

Hi, I'm still trying to get used to this whole process so its fairly new to me. Can you please help me with breaking this down to get the derivative?

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

Thanks

 

[Deleted member 4993]

Hi, I'm still trying to get used to this whole process so its fairly new to me. Can you please help me with breaking this down to get the derivative?

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

Thanks

As suggested by the title, take logarithm of both sides. What do you get?

 

[dubb]

This is what i get.

Lny = sin^2(x)Ln(x+x^2) not sure what to do next. Chain rule of Ln(x+x^2)?

 

[Deleted member 4993]

This is what i get.

Lny = sin^2(x) * Ln(x+x^2) not sure what to do next. Chain rule of Ln(x+x^2)?

Now differentiate both sides using chain rule and product rule.

 

[dubb]

I got:
1/y = 2cosxsinxLn(x+x^2) + (2xsine^2(x))/(x+x^2)

does that look right?