Question

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

Answer 1

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

Answer 2

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