Question

Найти производную второго порядка
у=tg(x^2)

Answer 1

$y=tg(x^2)\y`=frac{2x}{cos^2(x^2)}\y``=frac{2cos^2(x^2)+2x*2x*2cos(x^2)sin(x^2)}{cos^4(x^2)}=frac{2cos^2(x^2)+4x^2*sin(2x^2)}{cos^4(x^2)}$

Answer 2

$y=tg(x^2) \ y'=(tg(x^2) )'= frac{2x}{cos^2(x^2)} \ y''=( frac{2x}{cos^2(x^2)})'=frac{2cos^2(x^2)+2x*2cos(x^2)sin(x^2)*2x}{cos^4(x^2)}= frac{2cos^2(x^2)+4x^2sin(2x^2)}{cos^4(x^2)}$