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#