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

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:
y'=1/(tan(x^2)]*1/(cos^2(x^2))*2x=(2x)/(sin(x^2)cos(x^2)
(Where $\tan \left({x}^{2}\right) = \sin \frac{{x}^{2}}{\cos} \left({x}^{2}\right)$)