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

1 Answer
Jim G. · John D.
Mar 20, 2017

#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)#

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