How do you differentiate #y=cos^2(x^2-2)#?

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Answer 1 · 2017-02-25T06:57:41

#y'=-4xsin(x^2-2)cos(x^2-2)#

You would use the power rule:

#f(x)=x^n->f'(x)=n*x^(n-1)#

#f(x)=g(x)^n->f'(x)=n*g(x)^(n-1)*g'(x)#

#f(x)=cos(g(x))->f'(x)=-sin(g(x))*g'(x)#

Then it is:

#y'=2cos(x^2-2)*(-sin(x^2-2))*2x#

#y'=-4xsin(x^2-2)cos(x^2-2)#