en

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

derivative of (4x^3+6/x)

Solution

\frac{d}{d x} (\frac{4 x ^{3} + 6}{x})

Solution

\frac{8 x ^{3} - 6}{x ^{2}}

Solution steps

\frac{d}{d x} (\frac{4 x ^{3} + 6}{x})

Apply the Quotient Rule:

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

= \frac{\frac{d}{d x} ( 4 x ^{3} + 6 ) x - \frac{d x}{d x} ( 4 x ^{3} + 6 )}{x ^{2}}

\frac{d}{d x} (4 x^{3} + 6) = 12 x^{2}

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

= \frac{12 x ^{2} x - 1 \cdot ( 4 x ^{3} + 6 )}{x ^{2}}

Simplify

\frac{12 x ^{2} x - 1 \cdot ( 4 x ^{3} + 6 )}{x ^{2}} : \frac{8 x ^{3} - 6}{x ^{2}}

= \frac{8 x ^{3} - 6}{x ^{2}}

Popular Examples

integral from 25 to 50 of 15

\int_{25}^{50} 15 d x

derivative of 3e^x+ln(x+tan(x))

\frac{d}{d x} (3 e^{x} + ln (x) + tan (x))

limit as t approaches 0 of 7/t-7/(t^2+t)

t \to 0 lim (\frac{7}{t} - \frac{7}{t ^{2} + t})

limit as x approaches 2 of (x^2)/(x-2)

x \to 2 lim (\frac{x ^{2}}{x - 2})

limit as x approaches infinity of \sqrt[7]{x}

Frequently Asked Questions (FAQ)

What is the derivative of (4x^3+6/x) ?
The derivative of (4x^3+6/x) is (8x^3-6)/(x^2)
What is the first derivative of (4x^3+6/x) ?
The first derivative of (4x^3+6/x) is (8x^3-6)/(x^2)