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Popular >

derivative of (cos(t))/t

Solution

derivative of

\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 of e^{(3x)}

\int e^{(3 x)} d x

integral of (x+3)/((x-2)(x+5))

\int \frac{x + 3}{( x - 2 ) ( x + 5 )} d x

(\partial)/(\partial x)((x-1)^{2/3}(y^2-4))

\frac{\partial}{\partial x} ((x - 1)^{\frac{2}{3}} (y^{2} - 4))

(\partial)/(\partial y)(y(x+y+1))

\frac{\partial}{\partial y} (y (x + y + 1))

derivative of (x-5^3)

\frac{d}{d x} ((x - 5)^{3})

Frequently Asked Questions (FAQ)

What is the derivative of (cos(t))/t ?
The derivative of (cos(t))/t is (-tsin(t)-cos(t))/(t^2)
What is the first derivative of (cos(t))/t ?
The first derivative of (cos(t))/t is (-tsin(t)-cos(t))/(t^2)