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

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

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

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

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

cos (wt) w

Solution steps

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

Treat

w

as a constant

Apply the chain rule:

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

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

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

= cos (wt) w

in v erse l a pl a ce \frac{1}{s ^{3} + 6 s}

\frac{d y}{d x} = \frac{x y + x ^{2} e ^{\frac{y}{x}}}{x ^{2}}

\int - 20

2 y^{^{'}} + y = \frac{e ^{2 x}}{2}

x^{2} y^{^{'}} = y - x y, y (- 1) = - 1