en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

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

Popular Examples

integral from 2 to 5 of e^{-x}

\int_{2}^{5} e^{- x} d x

(\partial)/(\partial y)(3y^2cos(4x))

\frac{\partial}{\partial y} (3 y^{2} cos (4 x))

(4+x)(dy)/(dx)+y=4+x

(4 + x) \frac{d y}{d x} + y = 4 + x

(\partial)/(\partial y)(-6xy)

\frac{\partial}{\partial y} (- 6 x y)

derivative of 5/(sqrt(x))derivative of

\frac{5}{x}

Frequently Asked Questions (FAQ)

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