What is the derivative of (cos(x)/(2x)) ?

The derivative of (cos(x)/(2x)) is (-xsin(x)-cos(x))/(2x^2)

What is the first derivative of (cos(x)/(2x)) ?

The first derivative of (cos(x)/(2x)) is (-xsin(x)-cos(x))/(2x^2)

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\frac{d}{d x} (\frac{cos ( x )}{2 x})

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

Solution steps

\frac{d}{d x} (\frac{cos ( x )}{2 x})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{2} \frac{d}{d x} (\frac{cos ( x )}{x})

Apply the Quotient Rule:

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

= \frac{1}{2} \cdot \frac{\frac{d}{d x} ( cos ( x ) ) x - \frac{d x}{d x} cos ( x )}{x ^{2}}

\frac{d}{d x} (cos (x)) = - sin (x)

\frac{d x}{d x} = 1

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

Simplify

\frac{1}{2} \cdot \frac{( - sin ( x ) ) x - 1 \cdot cos ( x )}{x ^{2}} : \frac{- x sin ( x ) - cos ( x )}{2 x ^{2}}

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

\int \frac{sec ^{3} ( x )}{2} d x

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

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

x \to 0 lim (x^{2} + 2 x)

\int x^{- 0.5} d x

What is the derivative of (cos(x)/(2x)) ?
The derivative of (cos(x)/(2x)) is (-xsin(x)-cos(x))/(2x^2)
What is the first derivative of (cos(x)/(2x)) ?
The first derivative of (cos(x)/(2x)) is (-xsin(x)-cos(x))/(2x^2)