What is the d/(dt)((cos(t))^2) ?

The d/(dt)((cos(t))^2) is -sin(2t)

What is the first d/(dt)((cos(t))^2) ?

The first d/(dt)((cos(t))^2) is -sin(2t)

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\frac{d}{d t} ((cos (t))^{2})

- sin (2 t)

Solution steps

\frac{d}{d t} ((cos (t))^{2})

Apply the chain rule:

2 cos (t) \frac{d}{d t} (cos (t))

= 2 cos (t) \frac{d}{d t} (cos (t))

\frac{d}{d t} (cos (t)) = - sin (t)

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

Simplify

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

= - sin (2 t)

\frac{\partial}{\partial y} (x y e^{- 4 y})

\int \frac{1}{x 7 - x ^{2}} d x

\int 4 x - 2 d x

\frac{3}{s ^{2} + 2 s + 10}

\frac{1}{s ( s ^{2} + 2 )}