What is the derivative of (1-cos(x)/x) ?

The derivative of (1-cos(x)/x) is (xsin(x)-1+cos(x))/(x^2)

What is the first derivative of (1-cos(x)/x) ?

The first derivative of (1-cos(x)/x) is (xsin(x)-1+cos(x))/(x^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{1 - cos ( x )}{x})

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

Solution steps

\frac{d}{d x} (\frac{1 - cos ( x )}{x})

Apply the Quotient Rule:

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

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

\frac{d}{d x} (1 - cos (x)) = sin (x)

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

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

Simplify

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

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

\int \frac{2 x - 1}{2 x + 3} d x

\frac{d}{d x} (ln (x + 2 y + 3 z))

y^{^{'''}} = e^{- 0.2 x}

\frac{( s + 2 )}{( s ^{2} + 4 )}

(x^{2} + 4) (2 x - 6)

What is the derivative of (1-cos(x)/x) ?
The derivative of (1-cos(x)/x) is (xsin(x)-1+cos(x))/(x^2)
What is the first derivative of (1-cos(x)/x) ?
The first derivative of (1-cos(x)/x) is (xsin(x)-1+cos(x))/(x^2)