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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (\frac{5}{x + 8})

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

Solution steps

\frac{d}{d x} (\frac{5}{x + 8})

Take the constant out:

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

= 5 \frac{d}{d x} (\frac{1}{x + 8})

Apply exponent rule:

\frac{1}{a} = a^{- 1}

= 5 \frac{d}{d x} ((x + 8)^{- 1})

Apply the chain rule:

- \frac{1}{( x + 8 ) ^{2}} \frac{d}{d x} (x + 8)

= - \frac{1}{( x + 8 ) ^{2}} \frac{d}{d x} (x + 8)

\frac{d}{d x} (x + 8) = 1

= 5 (- \frac{1}{( x + 8 ) ^{2}} \cdot 1)

Simplify

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

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

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