Mathematics, 20.08.2019 16:00 ujusdied3912
What is the derivative of y=sec(x2)y=sec(x^2)?
Answers: 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)}](/tpl/images/0182/0588/a4845.png)
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