What is the derivative of f(x)=(2x)/((x^3-8)^2) ?

The derivative of f(x)=(2x)/((x^3-8)^2) is (2(-5x^3-8))/((x^3-8)^3)

What is the first derivative of f(x)=(2x)/((x^3-8)^2) ?

The first derivative of f(x)=(2x)/((x^3-8)^2) is (2(-5x^3-8))/((x^3-8)^3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

f (x) = \frac{2 x}{( x ^{3} - 8 ) ^{2}}

\frac{2 ( - 5 x ^{3} - 8 )}{( x ^{3} - 8 ) ^{3}}

Solution steps

\frac{d}{d x} (\frac{2 x}{( x ^{3} - 8 ) ^{2}})

Take the constant out:

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

= 2 \frac{d}{d x} (\frac{x}{( x ^{3} - 8 ) ^{2}})

Apply the Quotient Rule:

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

= 2 \cdot \frac{\frac{d x}{d x} ( x ^{3} - 8 ) ^{2} - \frac{d}{d x} ( ( x ^{3} - 8 ) ^{2} ) x}{( ( x ^{3} - 8 ) ^{2} ) ^{2}}

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

\frac{d}{d x} ((x^{3} - 8)^{2}) = 6 x^{2} (x^{3} - 8)

= 2 \cdot \frac{1 \cdot ( x ^{3} - 8 ) ^{2} - 6 x ^{2} ( x ^{3} - 8 ) x}{( ( x ^{3} - 8 ) ^{2} ) ^{2}}

Simplify

2 \cdot \frac{1 \cdot ( x ^{3} - 8 ) ^{2} - 6 x ^{2} ( x ^{3} - 8 ) x}{( ( x ^{3} - 8 ) ^{2} ) ^{2}} : \frac{2 ( - 5 x ^{3} - 8 )}{( x ^{3} - 8 ) ^{3}}

= \frac{2 ( - 5 x ^{3} - 8 )}{( x ^{3} - 8 ) ^{3}}

cos (x^{4})

(- sin (3 x) \cdot 3)^{^{'}}

x \to \infty lim (\frac{( e ^{2 x} )}{x ^{2}})

\frac{d y}{d x} = \frac{x}{y} + \frac{y}{x}

\frac{\partial}{\partial x} ((x^{2} + 2 y^{2} + 3 z^{2}) e^{- (x^{2} + y^{2} + z^{2})})

What is the derivative of f(x)=(2x)/((x^3-8)^2) ?
The derivative of f(x)=(2x)/((x^3-8)^2) is (2(-5x^3-8))/((x^3-8)^3)
What is the first derivative of f(x)=(2x)/((x^3-8)^2) ?
The first derivative of f(x)=(2x)/((x^3-8)^2) is (2(-5x^3-8))/((x^3-8)^3)