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

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

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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of

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

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

Solution steps

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

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

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

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

Simplify

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

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

x \to - 2 lim (2 + x)

x \to 0 lim (\frac{x - 1}{x})

\int \frac{4}{x ^{2} - x - 6} d x

\int 2 x + 2 d x

6 + 5 x

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