What is the first (cos^2(t))^' ?

The first (cos^2(t))^' is -sin(2t)

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(cos^2(t))^'

(cos^{2} (t))^{^{'}}

- sin (2 t)

Solution steps

(cos^{2} (t))^{'}

Apply the chain rule:

2 cos (t) (cos (t))^{'}

= 2 cos (t) (cos (t))^{'}

(cos (t))^{'} = - sin (t)

= 2 cos (t) (- sin (t))

Simplify

2 cos (t) (- sin (t)) : - sin (2 t)

= - sin (2 t)

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