What is the derivative of (x^2-8x+5)/(x^2+8) ?

The derivative of (x^2-8x+5)/(x^2+8) is (8x^2+6x-64)/((x^2+8)^2)

What is the first derivative of (x^2-8x+5)/(x^2+8) ?

The first derivative of (x^2-8x+5)/(x^2+8) is (8x^2+6x-64)/((x^2+8)^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

\frac{x ^{2} - 8 x + 5}{x ^{2} + 8}

\frac{8 x ^{2} + 6 x - 64}{( x ^{2} + 8 ) ^{2}}

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Expand

(2 x - 8) (x^{2} + 8) - 2 x (x^{2} - 8 x + 5) : 8 x^{2} + 6 x - 64

= \frac{8 x ^{2} + 6 x - 64}{( x ^{2} + 8 ) ^{2}}

\int \frac{1}{4 x x ^{2} - 16} d x

\frac{d}{d x} (1 - cos (5 x))

x \to 1 lim (\frac{x + 3}{x + 1})

- 6 t^{2} δ (t - 5)

5 - 5 x^{3}

What is the derivative of (x^2-8x+5)/(x^2+8) ?
The derivative of (x^2-8x+5)/(x^2+8) is (8x^2+6x-64)/((x^2+8)^2)
What is the first derivative of (x^2-8x+5)/(x^2+8) ?
The first derivative of (x^2-8x+5)/(x^2+8) is (8x^2+6x-64)/((x^2+8)^2)