What is the derivative of (2x/(7x^2+1)) ?

The derivative of (2x/(7x^2+1)) is (2(-7x^2+1))/((7x^2+1)^2)

What is the first derivative of (2x/(7x^2+1)) ?

The first derivative of (2x/(7x^2+1)) is (2(-7x^2+1))/((7x^2+1)^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}{7 x ^{2} + 1})

\frac{2 ( - 7 x ^{2} + 1 )}{( 7 x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{2 x}{7 x ^{2} + 1})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{x}{7 x ^{2} + 1})

Apply the Quotient Rule:

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

= 2 \cdot \frac{\frac{d x}{d x} ( 7 x ^{2} + 1 ) - \frac{d}{d x} ( 7 x ^{2} + 1 ) x}{( 7 x ^{2} + 1 ) ^{2}}

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

\frac{d}{d x} (7 x^{2} + 1) = 14 x

= 2 \cdot \frac{1 \cdot ( 7 x ^{2} + 1 ) - 14 xx}{( 7 x ^{2} + 1 ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( 7 x ^{2} + 1 ) - 14 xx}{( 7 x ^{2} + 1 ) ^{2}} : \frac{2 ( - 7 x ^{2} + 1 )}{( 7 x ^{2} + 1 ) ^{2}}

= \frac{2 ( - 7 x ^{2} + 1 )}{( 7 x ^{2} + 1 ) ^{2}}

y^{^{''}} + 256 y = sec (16 x)

y = 12 (x - \frac{1}{x})^{2}, at x = 2

y = 4 x cos (x^{2})

\int (2 e^{9 x}) d x

\frac{d}{d x} (\frac{( x - 1 )}{( x - 2 )})

What is the derivative of (2x/(7x^2+1)) ?
The derivative of (2x/(7x^2+1)) is (2(-7x^2+1))/((7x^2+1)^2)
What is the first derivative of (2x/(7x^2+1)) ?
The first derivative of (2x/(7x^2+1)) is (2(-7x^2+1))/((7x^2+1)^2)