How do you differentiate # y=sec (3x^2 - x)# using the chain rule?

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Answer 1 · 2015-12-11T00:22:03

#y'=(6x-1)sec(3x^2-x)tan(3x^2-x)#

Note that according to the chain rule #d/dx[sec(u)]=u'sec(u)tan(u)#.

Therefore

#d/dx[sec(3x^2-x)]=sec(3x^2-x)tan(3x^2-x)d/dx[3x^2-x]#

Find the derivative.

#d/dx[3x^2-x]=6x-1#

Plug this back in.

#y'=(6x-1)sec(3x^2-x)tan(3x^2-x)#