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

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

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

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

- \frac{9}{2 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x + 9}{2 x})

Take the constant out:

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

= \frac{1}{2} \frac{d}{d x} (\frac{2 x + 9}{x})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= - \frac{9}{2 x ^{2}}

f (x) = x^{2} + x - 2

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

\int cos (x) a^{s i n (x)} d x

\frac{\partial}{\partial x} (\frac{x}{yz})

\int (\frac{1}{1 + e ^{x}}) d x

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