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

The d/(dt)((sin(t))/t) is (tcos(t)-sin(t))/(t^2)

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

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

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

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

\int \frac{x - 1}{3 x ^{2} - 4 x + 3} d x

\int \frac{x + 3}{x ^{2} - 3 x + 2} d x

n = 5 \sum \infty e^{\frac{1}{n}}

\int csc (π x) cos (π x) d x

\int cos (nπ t) d t

What is the d/(dt)((sin(t))/t) ?
The d/(dt)((sin(t))/t) is (tcos(t)-sin(t))/(t^2)
What is the first d/(dt)((sin(t))/t) ?
The first d/(dt)((sin(t))/t) is (tcos(t)-sin(t))/(t^2)