How do I find the derivative of y = sin(tan x²)?

Use the chain rule, i.e.,

d/dx f(g(x))=f′(g(x))×g′(x)

= cos(tanx²) d/dx (tanx²)

= cos(tanx²) • sec2(x²) • 2x

Here is the similar question with complete solution

Derivatives of Trig Functions