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

The derivative of (x^2-1/(3x)) is (x^2+1)/(3x^2)

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\frac{x ^{2} + 1}{3 x ^{2}}

Solution steps

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

Take the constant out:

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

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

Apply the Quotient Rule:

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

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

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

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

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

Simplify

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

= \frac{x ^{2} + 1}{3 x ^{2}}

\int e^{- a t} d t

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

x \to \infty lim (1.3 x)

\int 7 sin (8 x) cos (5 x) d x

\frac{2}{s} - \frac{1}{s ^{3}}

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