What is the derivative of (6x)/((x^2+3)^2) ?

The derivative of (6x)/((x^2+3)^2) is (18(-x^2+1))/((x^2+3)^3)

What is the first derivative of (6x)/((x^2+3)^2) ?

The first derivative of (6x)/((x^2+3)^2) is (18(-x^2+1))/((x^2+3)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{6 x}{( x ^{2} + 3 ) ^{2}}

\frac{18 ( - x ^{2} + 1 )}{( x ^{2} + 3 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{6 x}{( x ^{2} + 3 ) ^{2}})

Take the constant out:

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

= 6 \frac{d}{d x} (\frac{x}{( x ^{2} + 3 ) ^{2}})

Apply the Quotient Rule:

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

= 6 \cdot \frac{\frac{d x}{d x} ( x ^{2} + 3 ) ^{2} - \frac{d}{d x} ( ( x ^{2} + 3 ) ^{2} ) x}{( ( x ^{2} + 3 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((x^{2} + 3)^{2}) = 4 x (x^{2} + 3)

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

Simplify

6 \cdot \frac{1 \cdot ( x ^{2} + 3 ) ^{2} - 4 x ( x ^{2} + 3 ) x}{( ( x ^{2} + 3 ) ^{2} ) ^{2}} : \frac{18 ( - x ^{2} + 1 )}{( x ^{2} + 3 ) ^{3}}

= \frac{18 ( - x ^{2} + 1 )}{( x ^{2} + 3 ) ^{3}}

y = 7^{x + a r c c o s (x)}

x^{2} - 4 x, 2 x - x^{2}

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

\frac{d}{d x} (ln (2 + e^{x}))

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

What is the derivative of (6x)/((x^2+3)^2) ?
The derivative of (6x)/((x^2+3)^2) is (18(-x^2+1))/((x^2+3)^3)
What is the first derivative of (6x)/((x^2+3)^2) ?
The first derivative of (6x)/((x^2+3)^2) is (18(-x^2+1))/((x^2+3)^3)