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

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

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

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

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

sin (2 t)

Solution steps

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

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

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

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)

\int \frac{x ^{9}}{1 + x ^{20}} d x

4 e^{- 3 t + 2}

x \to \infty lim (- \frac{4}{x})

\int \frac{e ^{x}}{2 x} d x

x \to - 1 lim (6)