en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ln|tan(x|)

Solution

\frac{d}{d x} (ln ∣ tan (x) ∣)

Solution

2 csc (2 x)

Solution steps

\frac{d}{d x} (ln ∣ tan (x) ∣)

Apply the chain rule:

\frac{1}{∣ tan ( x ) ∣} \frac{d}{d x} (∣ tan (x) ∣)

= \frac{1}{∣ tan ( x ) ∣} \frac{d}{d x} (∣ tan (x) ∣)

\frac{d}{d x} (∣ tan (x) ∣) = \frac{sec ^{2} ( x ) tan ( x )}{∣ tan ( x ) ∣}

= \frac{1}{∣ tan ( x ) ∣} \cdot \frac{sec ^{2} ( x ) tan ( x )}{∣ tan ( x ) ∣}

Simplify

\frac{1}{∣ tan ( x ) ∣} \cdot \frac{sec ^{2} ( x ) tan ( x )}{∣ tan ( x ) ∣} : 2 csc (2 x)

= 2 csc (2 x)

Popular Examples

area 1/(x+1),((x-1))/2 ,0,4 area

\frac{1}{x + 1}, \frac{( x - 1 )}{2}, 0, 4

derivative of 3x^x

\frac{d}{d x} (3 x^{x})

x y + y^{^{'}} = 92 x

derivative of sin(x/2-e^{-x^3})

\frac{d}{d x} (sin (\frac{x}{2}) - e^{- x^{3}})

(\partial)/(\partial x)((y/(x-y))^6)

\frac{\partial}{\partial x} ((\frac{y}{x - y})^{6})

Frequently Asked Questions (FAQ)

What is the derivative of ln|tan(x|) ?
The derivative of ln|tan(x|) is 2csc(2x)
What is the first derivative of ln|tan(x|) ?
The first derivative of ln|tan(x|) is 2csc(2x)