Answer:
[tex]2 (tanx^2)(sec^2x^2)(2x)[/tex]
Step-by-step explanation:
Quick reminder: since [tex]tan x = \frac{sinx}{cos x} \rightarrow Dtanx = \frac1{cos^2x}=sec^2x[/tex]
At this point, It's nested function over nested function over nested function, with the most internal one being the quadratic [tex]x^2[/tex], then the tangent, and then, most external one, it's the tangent squared.
Chain rule. The derivative of the outermost function is [tex]Df=2 (tan (x^2) )(Dtanx^2) = 2(tanx^2)(sec^2 (x^2)) (Dx^2) = \\ 2 (tanx^2)(sec^2x^2)(2x)[/tex]
Can you write it in a better form? Maybe. Is it needed? Honestly no.
