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

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

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

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

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} - 3 x + 1}{x ^{2}})

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

Solution steps

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

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

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

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

Simplify

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

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

x \to - 1 lim (8 x^{4} - 3 x^{3} + 7 x)

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

\frac{\partial}{\partial x} (ln (x + y))

f (u) = u^{2}

\frac{1}{3 + x}

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