Question

What is the derivative of `tan(x^2)`?

Answer 1

`y=tan(x^2)=tan(u)`

`:. (dy)/(du)=sec^2(u)=sec^2(x^2)`

`u=x^2, :. (du)/(dx)=2x`

Use the chain rule...

`(dy)/(du)*(du)/(dx)=2x*sec^2(x^2)=(dy)/(dx)`

Remember that:

If `y=tanx`, `(dy)/(dx)=sec^2(x)`

It's a general rule.