What is the d/(dt)(cos(wt)) ?

The d/(dt)(cos(wt)) is -sin(wt)w

What is the first d/(dt)(cos(wt)) ?

The first d/(dt)(cos(wt)) is -sin(wt)w

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

- sin (wt) w

Solution steps

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

Treat

w

as a constant

Apply the chain rule:

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

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

\frac{d}{d t} (wt) = w

= - sin (wt) w

\int 2 e^{x} cos (x) d x

\frac{\partial}{\partial y} (e^{y})

\frac{\partial}{\partial x} (4 x y - x^{4} - y^{4} + 1)

\int_{0}^{x} e^{- t^{2}} d t

\frac{x + 1}{4 x ^{2} + 12 x + 2}