What is the derivative of 1/(x 3/2) ?

The derivative of 1/(x 3/2) is -2/(3x^2)

What is the first derivative of 1/(x 3/2) ?

The first derivative of 1/(x 3/2) is -2/(3x^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{1}{x \frac{3}{2}})

- \frac{2}{3 x ^{2}}

Solution steps

\frac{d}{d x} (\frac{1}{x \frac{3}{2}})

Take the constant out:

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

= \frac{1}{\frac{3}{2}} \frac{d}{d x} (\frac{1}{x})

Apply exponent rule:

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

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

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

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

Simplify

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

= - \frac{2}{3 x ^{2}}

What is the derivative of 1/(x 3/2) ?
The derivative of 1/(x 3/2) is -2/(3x^2)
What is the first derivative of 1/(x 3/2) ?
The first derivative of 1/(x 3/2) is -2/(3x^2)