What is the derivative of (7x)/((x^3-2)^2) ?

The derivative of (7x)/((x^3-2)^2) is (7(-5x^3-2))/((x^3-2)^3)

What is the first derivative of (7x)/((x^3-2)^2) ?

The first derivative of (7x)/((x^3-2)^2) is (7(-5x^3-2))/((x^3-2)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

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

\frac{7 ( - 5 x ^{3} - 2 )}{( x ^{3} - 2 ) ^{3}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

= 7 \cdot \frac{\frac{d x}{d x} ( x ^{3} - 2 ) ^{2} - \frac{d}{d x} ( ( x ^{3} - 2 ) ^{2} ) x}{( ( x ^{3} - 2 ) ^{2} ) ^{2}}

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

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

= 7 \cdot \frac{1 \cdot ( x ^{3} - 2 ) ^{2} - 6 x ^{2} ( x ^{3} - 2 ) x}{( ( x ^{3} - 2 ) ^{2} ) ^{2}}

Simplify

7 \cdot \frac{1 \cdot ( x ^{3} - 2 ) ^{2} - 6 x ^{2} ( x ^{3} - 2 ) x}{( ( x ^{3} - 2 ) ^{2} ) ^{2}} : \frac{7 ( - 5 x ^{3} - 2 )}{( x ^{3} - 2 ) ^{3}}

= \frac{7 ( - 5 x ^{3} - 2 )}{( x ^{3} - 2 ) ^{3}}

What is the derivative of (7x)/((x^3-2)^2) ?
The derivative of (7x)/((x^3-2)^2) is (7(-5x^3-2))/((x^3-2)^3)
What is the first derivative of (7x)/((x^3-2)^2) ?
The first derivative of (7x)/((x^3-2)^2) is (7(-5x^3-2))/((x^3-2)^3)