Question

Find the derivative of tan²x²​

Answer 1

`2 (tanx^2)(sec^2x^2)(2x)`

Explanation:

Quick reminder: since
`tan x = (sinx)/(cos x) \rightarrow Dtanx = \frac1{cos^2x}=sec^2x`

At this point, It's nested function over nested function over nested function, with the most internal one being the quadratic
`x^2`, then the tangent, and then, most external one, it's the tangent squared.

Chain rule. The derivative of the outermost function is
`Df=2 (tan (x^2) )(Dtanx^2) = 2(tanx^2)(sec^2 (x^2)) (Dx^2) = \\ 2 (tanx^2)(sec^2x^2)(2x)`

Can you write it in a better form? Maybe. Is it needed? Honestly no.