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

The derivative of 8/(|x-2|^3) is -(24)/(|x-2|(x-2)^3)

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

The first derivative of 8/(|x-2|^3) is -(24)/(|x-2|(x-2)^3)

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{8}{∣ x - 2 ∣ ^{3}})

- \frac{24}{∣ x - 2 ∣ ( x - 2 ) ^{3}}

Solution steps

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

Take the constant out:

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

= 8 \frac{d}{d x} (\frac{1}{∣ x - 2 ∣ ^{3}})

Apply exponent rule:

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

= 8 \frac{d}{d x} (∣ x - 2 ∣^{- 3})

Apply the chain rule:

- \frac{3}{∣ x - 2 ∣ ^{4}} \frac{d}{d x} (∣ x - 2 ∣)

= - \frac{3}{∣ x - 2 ∣ ^{4}} \frac{d}{d x} (∣ x - 2 ∣)

\frac{d}{d x} (∣ x - 2 ∣) = \frac{x - 2}{∣ x - 2 ∣}

= 8 (- \frac{3}{∣ x - 2 ∣ ^{4}} \cdot \frac{x - 2}{∣ x - 2 ∣})

Simplify

8 (- \frac{3}{∣ x - 2 ∣ ^{4}} \cdot \frac{x - 2}{∣ x - 2 ∣}) : - \frac{24}{∣ x - 2 ∣ ( x - 2 ) ^{3}}

= - \frac{24}{∣ x - 2 ∣ ( x - 2 ) ^{3}}

\int (2 x^{2} + 2 x - 3)^{10} \cdot (2 x + 1) d x

\frac{d}{d x} (\frac{9 - x ^{2} - y ^{2}}{x + z})

\frac{d}{d x} (cos (7 π x))

x \to 0 lim (\frac{x ^{- 2} - 6 ^{- 2}}{x + 6})

f (x) = 2 x + 3, [- 1, 2]

What is the derivative of 8/(|x-2|^3) ?
The derivative of 8/(|x-2|^3) is -(24)/(|x-2|(x-2)^3)
What is the first derivative of 8/(|x-2|^3) ?
The first derivative of 8/(|x-2|^3) is -(24)/(|x-2|(x-2)^3)