What is the derivative of 1/(3x^2-5/(2x)+8x-6) ?

The derivative of 1/(3x^2-5/(2x)+8x-6) is 5/(2x^2)-2/(3x^3)+8

What is the first derivative of 1/(3x^2-5/(2x)+8x-6) ?

The first derivative of 1/(3x^2-5/(2x)+8x-6) is 5/(2x^2)-2/(3x^3)+8

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

\frac{d}{d x} (\frac{1}{3 x ^{2}} - \frac{5}{2 x} + 8 x - 6)

\frac{5}{2 x ^{2}} - \frac{2}{3 x ^{3}} + 8

Solution steps

\frac{d}{d x} (\frac{1}{3 x ^{2}} - \frac{5}{2 x} + 8 x - 6)

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (\frac{1}{3 x ^{2}}) - \frac{d}{d x} (\frac{5}{2 x}) + \frac{d}{d x} (8 x) - \frac{d}{d x} (6)

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

\frac{d}{d x} (\frac{5}{2 x}) = - \frac{5}{2 x ^{2}}

\frac{d}{d x} (8 x) = 8

\frac{d}{d x} (6) = 0

= - \frac{2}{3 x ^{3}} - (- \frac{5}{2 x ^{2}}) + 8 - 0

Simplify

= \frac{5}{2 x ^{2}} - \frac{2}{3 x ^{3}} + 8

What is the derivative of 1/(3x^2-5/(2x)+8x-6) ?
The derivative of 1/(3x^2-5/(2x)+8x-6) is 5/(2x^2)-2/(3x^3)+8
What is the first derivative of 1/(3x^2-5/(2x)+8x-6) ?
The first derivative of 1/(3x^2-5/(2x)+8x-6) is 5/(2x^2)-2/(3x^3)+8