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Popular >

derivative of f(t)=(cos(t))/t

Solution

derivative of

f (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

(1/(x^2)du)/(dx)-(2u)/(x^3)=-1/(x^2)

\frac{\frac{1}{x ^{2}} d u}{d x} - \frac{2 u}{x ^{3}} = - \frac{1}{x ^{2}}

integral of (x+1/x)^2

\int (x + \frac{1}{x})^{2} d x

y^{^{'}} = x y^{3}

4y^{''}+6y^'-y=5

4 y^{^{''}} + 6 y^{^{'}} - y = 5

derivative of-(6x/(x^2+1))

\frac{d}{d x} (- \frac{6 x}{x ^{2} + 1})

Frequently Asked Questions (FAQ)

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