What is the d/(dt)(((sin(t)))/((1-cos(t)))) ?

The d/(dt)(((sin(t)))/((1-cos(t)))) is 1/(-1+cos(t))

What is the first d/(dt)(((sin(t)))/((1-cos(t)))) ?

The first d/(dt)(((sin(t)))/((1-cos(t)))) is 1/(-1+cos(t))

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\frac{d}{d t} (\frac{( sin ( t ) )}{( 1 - cos ( t ) )})

\frac{1}{- 1 + cos ( t )}

Solution steps

\frac{d}{d t} (\frac{( sin ( t ) )}{( 1 - cos ( t ) )})

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d t} ( sin ( t ) ) ( 1 - cos ( t ) ) - \frac{d}{d t} ( 1 - cos ( t ) ) sin ( t )}{( 1 - cos ( t ) ) ^{2}}

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

\frac{d}{d t} (1 - cos (t)) = sin (t)

= \frac{cos ( t ) ( 1 - cos ( t ) ) - sin ( t ) sin ( t )}{( 1 - cos ( t ) ) ^{2}}

Simplify

\frac{cos ( t ) ( 1 - cos ( t ) ) - sin ( t ) sin ( t )}{( 1 - cos ( t ) ) ^{2}} : \frac{1}{- 1 + cos ( t )}

= \frac{1}{- 1 + cos ( t )}

What is the d/(dt)(((sin(t)))/((1-cos(t)))) ?
The d/(dt)(((sin(t)))/((1-cos(t)))) is 1/(-1+cos(t))
What is the first d/(dt)(((sin(t)))/((1-cos(t)))) ?
The first d/(dt)(((sin(t)))/((1-cos(t)))) is 1/(-1+cos(t))