en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of f(x)=4x^{-1/2}

Solution

derivative of

f (x) = 4 x^{- \frac{1}{2}}

Solution

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

Solution steps

\frac{d}{d x} (4 x^{- \frac{1}{2}})

Take the constant out:

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

= 4 \frac{d}{d x} (x^{- \frac{1}{2}})

Apply the Power Rule:

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

= 4 (- \frac{1}{2} x^{- \frac{1}{2} - 1})

Simplify

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

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

Popular Examples

d/(dh)(1.18sqrt(h))

\frac{d}{d h} (1.18 h)

(\partial)/(\partial x)(((7x-8y))/(1x+2y))

\frac{\partial}{\partial x} (\frac{( 7 x - 8 y )}{1 x + 2 y})

derivative of (cos(x^2)/(x^2+1))

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

derivative of x/((x^2+1))

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

(\partial)/(\partial x)(x^{0.5}y^{0.5}z)

\frac{\partial}{\partial x} (x^{0.5} y^{0.5} z)

Frequently Asked Questions (FAQ)

What is the derivative of f(x)=4x^{-1/2} ?
The derivative of f(x)=4x^{-1/2} is -2/(x^{3/2)}
What is the first derivative of f(x)=4x^{-1/2} ?
The first derivative of f(x)=4x^{-1/2} is -2/(x^{3/2)}