What is the derivative of x/(4x+9) ?

The derivative of x/(4x+9) is 9/((4x+9)^2)

What is the first derivative of x/(4x+9) ?

The first derivative of x/(4x+9) is 9/((4x+9)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{x}{4 x + 9}

\frac{9}{( 4 x + 9 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{x}{4 x + 9})

Apply the Quotient Rule:

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

= \frac{\frac{d x}{d x} ( 4 x + 9 ) - \frac{d}{d x} ( 4 x + 9 ) x}{( 4 x + 9 ) ^{2}}

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

\frac{d}{d x} (4 x + 9) = 4

= \frac{1 \cdot ( 4 x + 9 ) - 4 x}{( 4 x + 9 ) ^{2}}

Simplify

= \frac{9}{( 4 x + 9 ) ^{2}}

t an g e n t f (x) = e^{9 x} cos (π x), at x = 0

d er i v a t i v e 9 x^{8} e^{x} + e^{x} x^{9}

\int (x^{4} - e^{- 2 x}) d x

\int cos (t) tan (t) d t

\frac{d}{d x} (x^{4} e^{4 x})

What is the derivative of x/(4x+9) ?
The derivative of x/(4x+9) is 9/((4x+9)^2)
What is the first derivative of x/(4x+9) ?
The first derivative of x/(4x+9) is 9/((4x+9)^2)