en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of Ax^{-1/2}

Solution

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

Solution

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

Solution steps

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

Take the constant out:

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

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

Apply the Power Rule:

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

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

Simplify

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

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

Popular Examples

area x=y 1/3 ,x=0,y=64 area

x = y \frac{1}{3}, x = 0, y = 64

(y^2+yx)dx+x^2dy=0

(y^{2} + y x) d x + x^{2} d y = 0

derivative of (4x^5)/(e^{3x)}derivative of

\frac{4 x ^{5}}{e ^{3 x}}

limit as x approaches 0-of (e^x)/(1-e^x)

x \to 0 - lim (\frac{e ^{x}}{1 - e ^{x}})

derivative of f(x)=e^{-x}x-2e^{-x}derivative of

f (x) = e^{- x} x - 2 e^{- x}

Frequently Asked Questions (FAQ)

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