en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of ((x^3-x))/((x^2))

Solution

derivative of

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

Solution

\frac{x ^{2} + 1}{x ^{2}}

Solution steps

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

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

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

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

\frac{d}{d x} (x^{2}) = 2 x

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

Simplify

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

= \frac{x ^{2} + 1}{x ^{2}}

Graph

Popular Examples

derivative of (-2)/(x^3)derivative of

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

derivative of (sin^{22}(x)/(cos^2(x)))

\frac{d}{d x} (\frac{sin ^{22} ( x )}{cos ^{2} ( x )})

derivative of ((-48x))/((x^2-16)^2)derivative of

\frac{( - 48 x )}{( x ^{2} - 16 ) ^{2}}

derivative of sin(cos(x^2))derivative of

sin (cos (x^{2}))

derivative of 3*e^{-0.25*x^2}derivative of

3 \cdot e^{- 0.25 \cdot x^{2}}

Frequently Asked Questions (FAQ)

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