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

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

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

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

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

2 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:

- sin (2 t) \frac{d}{d t} (2 t)

= - sin (2 t) \frac{d}{d t} (2 t)

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

= - (- sin (2 t) \cdot 2)

Simplify

= 2 sin (2 t)

y = x^{8} e^{- x}, (1, \frac{1}{e})

\int (2 x^{4} - 8 x^{3}) \cdot e^{- 3 x} d x

\frac{d}{d x} (\frac{2 cos ( x )}{sec ( x )})

y^{^{''}} + y^{^{'}} + 6 y = 0, y (0) = 0, y^{^{'}} (0) = 0

(2 x y) d y + (x^{2} + y^{2}) d x = 0