What is the derivative of-A/(2x^{3/2}) ?

The derivative of-A/(2x^{3/2}) is (3A)/(4x^{5/2)}

What is the first derivative of-A/(2x^{3/2}) ?

The first derivative of-A/(2x^{3/2}) is (3A)/(4x^{5/2)}

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\frac{3 A}{4 x ^{\frac{5}{2}}}

Solution steps

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

Take the constant out:

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

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

Apply exponent rule:

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

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

Apply the Power Rule:

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

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

Simplify

- \frac{A}{2} (- \frac{3}{2} x^{- \frac{3}{2} - 1}) : \frac{3 A}{4 x ^{\frac{5}{2}}}

= \frac{3 A}{4 x ^{\frac{5}{2}}}

What is the derivative of-A/(2x^{3/2}) ?
The derivative of-A/(2x^{3/2}) is (3A)/(4x^{5/2)}
What is the first derivative of-A/(2x^{3/2}) ?
The first derivative of-A/(2x^{3/2}) is (3A)/(4x^{5/2)}