What is the derivative of (cos(x)/(4x)) ?

The derivative of (cos(x)/(4x)) is (-xsin(x)-cos(x))/(4x^2)

What is the first derivative of (cos(x)/(4x)) ?

The first derivative of (cos(x)/(4x)) is (-xsin(x)-cos(x))/(4x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

\frac{d}{d x} (\frac{cos ( x )}{4 x})

\frac{- x sin ( x ) - cos ( x )}{4 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{cos ( x )}{4 x})

Take the constant out:

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

= \frac{1}{4} \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}{4} \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}{4} \cdot \frac{( - sin ( x ) ) x - 1 \cdot cos ( x )}{x ^{2}}

Simplify

\frac{1}{4} \cdot \frac{( - sin ( x ) ) x - 1 \cdot cos ( x )}{x ^{2}} : \frac{- x sin ( x ) - cos ( x )}{4 x ^{2}}

= \frac{- x sin ( x ) - cos ( x )}{4 x ^{2}}

x \to 1 - lim (x^{3} - 4)

\int 5 - 3 (1 + x^{2})^{- 1} d x

y = (arctan (8 x))^{2}

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

\int \frac{sin ( 2 x )}{4 - cos ^{4} ( x )} d x

What is the derivative of (cos(x)/(4x)) ?
The derivative of (cos(x)/(4x)) is (-xsin(x)-cos(x))/(4x^2)
What is the first derivative of (cos(x)/(4x)) ?
The first derivative of (cos(x)/(4x)) is (-xsin(x)-cos(x))/(4x^2)