Question

How do you differentiate `ln (tan (x^2))`?

Answer 1

I would use the Chain Rule: first differentiating `ln` as it is then multiply by the `tan` differentiated as it is and at last times `x^2` differentiated:
You get:
`y'=1/(tan(x^2)]*1/(cos^2(x^2))*2x=(2x)/(sin(x^2)cos(x^2)`

(Where `tan(x^2)=sin(x^2)/cos(x^2)`)