What is the derivative of (2x/(9-tan(x))) ?

The derivative of (2x/(9-tan(x))) is (2(9-tan(x)+xsec^2(x)))/((9-tan(x))^2)

What is the first derivative of (2x/(9-tan(x))) ?

The first derivative of (2x/(9-tan(x))) is (2(9-tan(x)+xsec^2(x)))/((9-tan(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{2 x}{9 - tan ( x )})

\frac{2 ( 9 - tan ( x ) + x sec ^{2} ( x ) )}{( 9 - tan ( x ) ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x}{9 - tan ( x )})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{x}{9 - tan ( x )})

Apply the Quotient Rule:

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

= 2 \cdot \frac{\frac{d x}{d x} ( 9 - tan ( x ) ) - \frac{d}{d x} ( 9 - tan ( x ) ) x}{( 9 - tan ( x ) ) ^{2}}

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

\frac{d}{d x} (9 - tan (x)) = - sec^{2} (x)

= 2 \cdot \frac{1 \cdot ( 9 - tan ( x ) ) - ( - sec ^{2} ( x ) ) x}{( 9 - tan ( x ) ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( 9 - tan ( x ) ) - ( - sec ^{2} ( x ) ) x}{( 9 - tan ( x ) ) ^{2}} : \frac{2 ( 9 - tan ( x ) + x sec ^{2} ( x ) )}{( 9 - tan ( x ) ) ^{2}}

= \frac{2 ( 9 - tan ( x ) + x sec ^{2} ( x ) )}{( 9 - tan ( x ) ) ^{2}}

n = 1 \sum \infty 4 (\frac{2}{3})^{n}

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

\int \frac{x ^{2} - 169}{x} d x

\frac{d}{d x} (\frac{- 2}{x ^{2}})

ln (1 + 5 x)

What is the derivative of (2x/(9-tan(x))) ?
The derivative of (2x/(9-tan(x))) is (2(9-tan(x)+xsec^2(x)))/((9-tan(x))^2)
What is the first derivative of (2x/(9-tan(x))) ?
The first derivative of (2x/(9-tan(x))) is (2(9-tan(x)+xsec^2(x)))/((9-tan(x))^2)