What is the derivative of ((3x+512/(x+1))^{2/3}) ?

The derivative of ((3x+512/(x+1))^{2/3}) is -(1018)/(3(3x+512)^{1/3)(x+1)^{5/3}}

What is the first derivative of ((3x+512/(x+1))^{2/3}) ?

The first derivative of ((3x+512/(x+1))^{2/3}) is -(1018)/(3(3x+512)^{1/3)(x+1)^{5/3}}

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{3 x + 512}{x + 1})^{\frac{2}{3}})

- \frac{1018}{3 ( 3 x + 512 ) ^{\frac{1}{3}} ( x + 1 ) ^{\frac{5}{3}}}

Solution steps

\frac{d}{d x} ((\frac{3 x + 512}{x + 1})^{\frac{2}{3}})

Apply the chain rule:

\frac{2}{3 ( \frac{3 x + 512}{x + 1} ) ^{\frac{1}{3}}} \frac{d}{d x} (\frac{3 x + 512}{x + 1})

= \frac{2}{3 ( \frac{3 x + 512}{x + 1} ) ^{\frac{1}{3}}} \frac{d}{d x} (\frac{3 x + 512}{x + 1})

\frac{d}{d x} (\frac{3 x + 512}{x + 1}) = - \frac{509}{( x + 1 ) ^{2}}

= \frac{2}{3 ( \frac{3 x + 512}{x + 1} ) ^{\frac{1}{3}}} (- \frac{509}{( x + 1 ) ^{2}})

Simplify

\frac{2}{3 ( \frac{3 x + 512}{x + 1} ) ^{\frac{1}{3}}} (- \frac{509}{( x + 1 ) ^{2}}) : - \frac{1018}{3 ( 3 x + 512 ) ^{\frac{1}{3}} ( x + 1 ) ^{\frac{5}{3}}}

= - \frac{1018}{3 ( 3 x + 512 ) ^{\frac{1}{3}} ( x + 1 ) ^{\frac{5}{3}}}

y y^{^{'}} = \frac{x}{x ^{2} + 1}, y (0) = - 2

\frac{d y}{d x} - \frac{y}{3 x} + \frac{x}{3 y} = 0

\int x sin^{2} (6 x) d x

\frac{d}{d x} (4 x^{3} - 46 x^{2} + 120 x)

\int \frac{1}{x} d x

What is the derivative of ((3x+512/(x+1))^{2/3}) ?
The derivative of ((3x+512/(x+1))^{2/3}) is -(1018)/(3(3x+512)^{1/3)(x+1)^{5/3}}
What is the first derivative of ((3x+512/(x+1))^{2/3}) ?
The first derivative of ((3x+512/(x+1))^{2/3}) is -(1018)/(3(3x+512)^{1/3)(x+1)^{5/3}}