How do you differentiate $cos^2(x^3)$ ?

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Answer 1 · 2017-04-25T03:44:40

$-6x^2 cosx^3 sinx^3$

Given: $cos^2(x^3) = (cos (x^3))^2$

Use the Chain Rule, incorporating the Power Rule and the derivative of the cosine:

Use the Power rule $(u^n)' = n u^(n-1) u' " and " (cos w)' = -sin (w) w'$

Let $w = x^3; w' = 3x^2$

Let $u = cos w; " " n = 2; " " u' = 2 (cos w)^1(-sin w)w'$

$u' = 2 cos(x^3)(-sin(x^3))3x^2$

Simplify and rearrange:

$u' = -6x^2 cosx^3 sinx^3$

How do you differentiate cos^2(x^3)cos^2(x^3)?