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Popular >

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

Solution

derivative of

f (t) = \frac{sin ( t )}{t}

Solution

\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}}

Popular Examples

integral of y/(e^{-y)}

\int \frac{y}{e ^{- y}} d y

f(x)=(xcos(x)-2pi)/(x-2pi)

f (x) = \frac{x cos ( x ) - 2 π}{x - 2 π}

((m^2+2)/(sqrt(2m^3+4)))^'

(\frac{m ^{2} + 2}{2 m ^{3} + 4})^{^{'}}

y^{''}+9y=4cos(2x)

y^{^{''}} + 9 y = 4 cos (2 x)

(\partial)/(\partial x)(2e^y)

\frac{\partial}{\partial x} (2 e^{y})

Frequently Asked Questions (FAQ)

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