Question

How do you find the derivative of `G(x)=int (tan(t^2))dt` from `[1,x^2]`?

Answer 1

`G(x)=int tant^2 \ dt qquad [1,x^2]`

`"ie " G(x)=int_1^(x^2) tant^2 \ dt`

From the FTC:

`G'(x)= tan((x^2)^2) (x^2)' = 2x \ tan x^4`