Question

What is the derivative of `sec^2(x^3)`?

Answer 1

`6x^2sec^2(x^3)tan(x^3)`

Explanation:

`color(orange)"Reminder " color(red)(bar(ul(|color(white)(2/2)color(black)(d/dx(secx)=secxtanx)color(white)(2/2)|)))`

`"Express "sec^2(x^3)=(sec(x^3))^2`

differentiate using the `color(blue)"chain rule"`

`d/dx(sec(x^3))^2`

`=2sec(x^3)xxd/dx(sec(x^3))xxd/dx(x^3)`

`=2sec(x^3)xxsec(x^3)tan(x^3)xx3x^2`

`=6x^2sec^2(x^3)tan(x^3)`