What is the derivative of ((8x^3-4x^2+3))/x ?

The derivative of ((8x^3-4x^2+3))/x is (16x^3-4x^2-3)/(x^2)

What is the first derivative of ((8x^3-4x^2+3))/x ?

The first derivative of ((8x^3-4x^2+3))/x is (16x^3-4x^2-3)/(x^2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

derivative of

\frac{( 8 x ^{3} - 4 x ^{2} + 3 )}{x}

\frac{16 x ^{3} - 4 x ^{2} - 3}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{8 x ^{3} - 4 x ^{2} + 3}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 8 x ^{3} - 4 x ^{2} + 3 ) x - \frac{d x}{d x} ( 8 x ^{3} - 4 x ^{2} + 3 )}{x ^{2}}

\frac{d}{d x} (8 x^{3} - 4 x^{2} + 3) = 24 x^{2} - 8 x

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

= \frac{( 24 x ^{2} - 8 x ) x - 1 \cdot ( 8 x ^{3} - 4 x ^{2} + 3 )}{x ^{2}}

Simplify

\frac{( 24 x ^{2} - 8 x ) x - 1 \cdot ( 8 x ^{3} - 4 x ^{2} + 3 )}{x ^{2}} : \frac{16 x ^{3} - 4 x ^{2} - 3}{x ^{2}}

= \frac{16 x ^{3} - 4 x ^{2} - 3}{x ^{2}}

What is the derivative of ((8x^3-4x^2+3))/x ?
The derivative of ((8x^3-4x^2+3))/x is (16x^3-4x^2-3)/(x^2)
What is the first derivative of ((8x^3-4x^2+3))/x ?
The first derivative of ((8x^3-4x^2+3))/x is (16x^3-4x^2-3)/(x^2)