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

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

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d t}{d t} = 1

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

Simplify

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

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