What is the first (cos^2(θ))^' ?

The first (cos^2(θ))^' is -sin(2θ)

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(cos^2(θ))^'

(cos^{2} (θ))^{^{'}}

- sin (2 θ)

Solution steps

(cos^{2} (θ))^{'}

Apply the chain rule:

2 cos (θ) (cos (θ))^{'}

= 2 cos (θ) (cos (θ))^{'}

(cos (θ))^{'} = - sin (θ)

= 2 cos (θ) (- sin (θ))

Simplify

2 cos (θ) (- sin (θ)) : - sin (2 θ)

= - sin (2 θ)

\frac{1}{1 - x}

\frac{d}{d x} (\frac{8 x}{3 - tan ( x )})

f (x) = 7 x + 2

\frac{d}{d x} (- x^{2})

\frac{d}{d x} (sec^{2} (x) tan (x))