en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (1+x/(x^3))

Solution

\frac{d}{d x} (\frac{1 + x}{x ^{3}})

Solution

\frac{- 2 x - 3}{x ^{4}}

Solution steps

\frac{d}{d x} (\frac{1 + x}{x ^{3}})

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{- 2 x - 3}{x ^{4}}

Popular Examples

(\partial)/(\partial x)(sqrt(xye^y))

\frac{\partial}{\partial x} (x y e^{y})

y^{^{'}} + 7 y = e^{6 x}

integral from 0 to 2pi of sin^2(x)

\int_{0}^{2 π} sin^{2} (x) d x

sum from n=1 to infinity of n^{-1/5}

n = 1 \sum \infty n^{- \frac{1}{5}}

limit as x approaches 2-of (5x)/(x-6)

x \to 2 - lim (\frac{5 x}{x - 6})

Frequently Asked Questions (FAQ)

What is the derivative of (1+x/(x^3)) ?
The derivative of (1+x/(x^3)) is (-2x-3)/(x^4)
What is the first derivative of (1+x/(x^3)) ?
The first derivative of (1+x/(x^3)) is (-2x-3)/(x^4)