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

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

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

The first derivative of (cos(ln(x))/x) is (-sin(ln(x))-cos(ln(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{cos ( ln ( x ) )}{x})

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

= \frac{( - \frac{s i n ( l n ( x ) )}{x} ) x - 1 \cdot cos ( ln ( x ) )}{x ^{2}}

Simplify

\frac{( - \frac{s i n ( l n ( x ) )}{x} ) x - 1 \cdot cos ( ln ( x ) )}{x ^{2}} : \frac{- sin ( ln ( x ) ) - cos ( ln ( x ) )}{x ^{2}}

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

x \to 3 lim (3 x - 3 a x + 2 a)

\frac{d}{d x} (x^{3} - 3 x^{2} - 24 x + 80)

\int \frac{x ^{5}}{1 + x ^{3}} d x

\int - 75 x^{2} + 600 x + C d x

\int x^{2} 3 + x^{3} d x

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