How do you differentiate $y = {cos}^{2} (x^{2} - 2)$ $y=cos^2(x^2-2)$ ?

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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:

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

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

How do you differentiate y=cos^2(x^2-2)y=cos2(x2−2)y=cos^2(x^2-2)?