Qual é a derivada de # y = sec (x ^ 2) #?

#y'=2x*sec(x^2)tan(x^2)#

Solution

let's #y=f(g(x))#

Using Chain Rule, we get

#y'=f'(g(x))*g'(x)#

for given problem, which is

#y=sec(x^2)#

differentiating with respect to #x# using Chain Rule,

#y'=sec(x^2)tan(x^2)*(x^2)'#

#y'=sec(x^2)tan(x^2)*2x#

#y'=2x*sec(x^2)tan(x^2)#