How do you differentiate # f(x) = sec(x^2 + 1)^2 #?

1 Answer
smartspot2
Jul 2, 2017

#f'(x)=4x*sec(x^2+1)^2*tan(x^2+1)#

Explanation:

#d/dx[sec(u)] = sec(u)*tan(u)*u'#

Using the above rule, we can differentiate:
#f(x)=sec(x^2+1)^2#
#f'(x)=2sec(x^2+1)*d/dx[sec(x^2+1)]#
#=2sec(x^2+1)*sec(x^2+1)*tan(x^2+1)*d/dx[x^2+1]#
#=2sec(x^2+1)*sec(x^2+1)*tan(x^2+1)*2x#

Simplifying gives:
#f'(x)=4x*sec(x^2+1)^2*tan(x^2+1)#

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