en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (1-2x/x)

Solution

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

Solution

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

Solution steps

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

Apply the Quotient Rule:

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

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

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

\frac{d x}{d x} = 1

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

Simplify

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

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

Popular Examples

derivative of cos(x-e^x)

\frac{d}{d x} (cos (x) - e^{x})

integral of tan^4(x/2)sec^4(x/2)

\int tan^{4} (\frac{x}{2}) sec^{4} (\frac{x}{2}) d x

integral of 1/(sqrt(9+y^2))

\int \frac{1}{9 + y ^{2}} d y

(\partial)/(\partial x)(sin(w/c x)sin(wt))

\frac{\partial}{\partial x} (sin (\frac{w}{c} x) sin (wt))

limit as t approaches 0 of (4e^t-4)/t

t \to 0 lim (\frac{4 e ^{t} - 4}{t})

Frequently Asked Questions (FAQ)

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