Question

What is the Derivative of y=sec(x2)y=sec(x^2)?

Answer 1

`y=\sec x^2\\ y'=\tan x^2 \sec x^2 \cdot2x\\ y=2x\tan x^2 \sec x^2`

Answer 2

`y=sec(x^2)=(1)/(cos(x^2))=[cos(x^2)]^(-1)\\\\y'=-cos(x^2)^(-2)\cdot[-sin(x^2)]\cdot2x\\\\=(1)/(cos^2(x^2))\cdot sin(x^2)\cdot2x=(2xsin(x^2))/(cos(x^2)cos(x^2))=2x\cdot(sin(x^2))/(cos(x^2))\cdot(1)/(cos(x^2))\\\\=\boxed{2xtg(x^2)sec(x^2)}`