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Popular >

d/(dt)((cos(t))/t)

Solution

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

Solution

\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}}

Popular Examples

integral from 0 to 1 of x^2e^{-x}

\int_{0}^{1} x^{2} e^{- x} d x

integral of (x-4)^3

\int (x - 4)^{3} d x

derivative of (tan(x)/(e^x))

\frac{d}{d x} (\frac{tan ( x )}{e ^{x}})

limit as x approaches-1 of (x+4)/(2x+1)

x \to - 1 lim (\frac{x + 4}{2 x + 1})

limit as x approaches 0 of (|x|-x)/x

x \to 0 lim (\frac{∣ x ∣ - x}{x})

Frequently Asked Questions (FAQ)

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)