What is the derivative of ((x^2+x(2x+1))/(4x)) ?

The derivative of ((x^2+x(2x+1))/(4x)) is x+3/4

What is the first derivative of ((x^2+x(2x+1))/(4x)) ?

The first derivative of ((x^2+x(2x+1))/(4x)) is x+3/4

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{( x ^{2} + x ) ( 2 x + 1 )}{4 x})

x + \frac{3}{4}

Solution steps

\frac{d}{d x} (\frac{( x ^{2} + x ) ( 2 x + 1 )}{4 x})

Take the constant out:

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

= \frac{1}{4} \frac{d}{d x} (\frac{( x ^{2} + x ) ( 2 x + 1 )}{x})

Apply the Quotient Rule:

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

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

\frac{d}{d x} ((x^{2} + x) (2 x + 1)) = 6 x^{2} + 6 x + 1

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

= \frac{1}{4} \cdot \frac{( 6 x ^{2} + 6 x + 1 ) x - 1 \cdot ( x ^{2} + x ) ( 2 x + 1 )}{x ^{2}}

Simplify

\frac{1}{4} \cdot \frac{( 6 x ^{2} + 6 x + 1 ) x - 1 \cdot ( x ^{2} + x ) ( 2 x + 1 )}{x ^{2}} : x + \frac{3}{4}

= x + \frac{3}{4}

\int 4 x - x e^{x} + e d x

\frac{\partial}{\partial y} (2 x y e^{x^{2}})

\frac{d}{d x} (- x^{4} cos (x))

n = 1 \sum \infty n^{n}

\int e^{4 x} sin (6 x) d x

What is the derivative of ((x^2+x(2x+1))/(4x)) ?
The derivative of ((x^2+x(2x+1))/(4x)) is x+3/4
What is the first derivative of ((x^2+x(2x+1))/(4x)) ?
The first derivative of ((x^2+x(2x+1))/(4x)) is x+3/4