What is the derivative of (4-4x-x^2/(x^2-6)) ?

The derivative of (4-4x-x^2/(x^2-6)) is (4x^2+4x+24)/((x^2-6)^2)

What is the first derivative of (4-4x-x^2/(x^2-6)) ?

The first derivative of (4-4x-x^2/(x^2-6)) is (4x^2+4x+24)/((x^2-6)^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{4 - 4 x - x ^{2}}{x ^{2} - 6})

\frac{4 x ^{2} + 4 x + 24}{( x ^{2} - 6 ) ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 - 4 x - x ^{2}}{x ^{2} - 6})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 - 4 x - x ^{2} ) ( x ^{2} - 6 ) - \frac{d}{d x} ( x ^{2} - 6 ) ( 4 - 4 x - x ^{2} )}{( x ^{2} - 6 ) ^{2}}

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

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

= \frac{( - 2 x - 4 ) ( x ^{2} - 6 ) - 2 x ( 4 - 4 x - x ^{2} )}{( x ^{2} - 6 ) ^{2}}

Expand

(- 2 x - 4) (x^{2} - 6) - 2 x (4 - 4 x - x^{2}) : 4 x^{2} + 4 x + 24

= \frac{4 x ^{2} + 4 x + 24}{( x ^{2} - 6 ) ^{2}}

\frac{2 x + 1}{( x ^{2} + 1 ) ^{1.5}}

x \to 0 lim (e^{\frac{1}{x ^{2}}})

x \to 0 - lim (x^{2} - 64)

x \to 0 lim (3 x + 6 x)

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

What is the derivative of (4-4x-x^2/(x^2-6)) ?
The derivative of (4-4x-x^2/(x^2-6)) is (4x^2+4x+24)/((x^2-6)^2)
What is the first derivative of (4-4x-x^2/(x^2-6)) ?
The first derivative of (4-4x-x^2/(x^2-6)) is (4x^2+4x+24)/((x^2-6)^2)