en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of pi/(sqrt(x))

Solution

\frac{d}{d x} (\frac{π}{x})

Solution

- \frac{π}{2 x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{π}{x})

Take the constant out:

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

= π \frac{d}{d x} (\frac{1}{x})

Apply exponent rule:

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

= π \frac{d}{d x} (x^{- \frac{1}{2}})

Apply the Power Rule:

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

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

Simplify

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

= - \frac{π}{2 x ^{\frac{3}{2}}}

Popular Examples

derivative of 5cos(pit)derivative of

5 cos (π t)

integral from 0 to 3 of (x+1)(2x-3)

\int_{0}^{3} (x + 1) (2 x - 3) d x

(\partial)/(\partial x)(4x^3y^3+3)

\frac{\partial}{\partial x} (4 x^{3} y^{3} + 3)

\frac{d}{d n} (2^{n})

longdivision (x-1)/(x+1)long division

\frac{x - 1}{x + 1}

Frequently Asked Questions (FAQ)

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