What is the derivative of f(x)=(3x)/(7x^2+1) ?

The derivative of f(x)=(3x)/(7x^2+1) is (3(-7x^2+1))/((7x^2+1)^2)

What is the first derivative of f(x)=(3x)/(7x^2+1) ?

The first derivative of f(x)=(3x)/(7x^2+1) is (3(-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

derivative of

f (x) = \frac{3 x}{7 x ^{2} + 1}

\frac{3 ( - 7 x ^{2} + 1 )}{( 7 x ^{2} + 1 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{3 x}{7 x ^{2} + 1})

Take the constant out:

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

= 3 \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}}

= 3 \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

= 3 \cdot \frac{1 \cdot ( 7 x ^{2} + 1 ) - 14 xx}{( 7 x ^{2} + 1 ) ^{2}}

Simplify

3 \cdot \frac{1 \cdot ( 7 x ^{2} + 1 ) - 14 xx}{( 7 x ^{2} + 1 ) ^{2}} : \frac{3 ( - 7 x ^{2} + 1 )}{( 7 x ^{2} + 1 ) ^{2}}

= \frac{3 ( - 7 x ^{2} + 1 )}{( 7 x ^{2} + 1 ) ^{2}}

What is the derivative of f(x)=(3x)/(7x^2+1) ?
The derivative of f(x)=(3x)/(7x^2+1) is (3(-7x^2+1))/((7x^2+1)^2)
What is the first derivative of f(x)=(3x)/(7x^2+1) ?
The first derivative of f(x)=(3x)/(7x^2+1) is (3(-7x^2+1))/((7x^2+1)^2)